|\^/| Maple 2016 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 4 then > printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel); > else > printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel, Re(value), Im(value), postlabel) else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value), Im(value), postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number -1 > if vallen = 5 then # if number 0 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 7 # Begin Function number 8 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number -1 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 0 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 1 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 2 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 3 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 3 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 2 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 8 # Begin Function number 9 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 2 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 3 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 4 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 5 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 6 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 6 > else > printf(" 0.0 Seconds\n"); > fi;# end if 5 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 9 # Begin Function number 10 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 10 # Begin Function number 11 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 5 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 6; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 5; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 11 # Begin Function number 12 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 5 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 6; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 5; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 12 # Begin Function number 13 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 16 # Begin Function number 17 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 17 # Begin Function number 18 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logitem_complex := proc(file,x) > fprintf(file,""); > fprintf(file,"%g + %g I",Re(x),Im(x)); > fprintf(file,""); > end; logitem_complex := proc(file, x) fprintf(file, ""); fprintf(file, "%g + %g I", Re(x), Im(x)); fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 5 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 6 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 7 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 8 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 9 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 10 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 11 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 11 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 20 # Begin Function number 21 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 21 # Begin Function number 22 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 22 # Begin Function number 23 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 11 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 11; > if (errflag) then # if number 11 > quit; > fi;# end if 11 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 23 # Begin Function number 24 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 11 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 12 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 12 > fi;# end if 11; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 24 # Begin Function number 25 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 11 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 11; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 25 # Begin Function number 26 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 11 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 26 # Begin Function number 27 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 11 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 27 # Begin Function number 28 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalc(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalc(in_val); ret end proc # End Function number 28 # Begin Function number 29 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 11 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 29 # Begin Function number 30 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 30 # Begin Function number 31 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 14 > if (rcs > glob__0) then # if number 15 > rad_c := float_abs( sqrt(rcs) * float_abs(glob_h)); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 13 > fi;# end if 12 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 11; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := float_abs(sqrt(rcs)*float_abs(glob_h)) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 31 # Begin Function number 32 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 32 # Begin Function number 33 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 33 # Begin Function number 34 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 11 > if (array_fact_1[nnn] = 0) then # if number 12 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 12; > else > ret := factorial_2(nnn); > fi;# end if 11; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 34 # Begin Function number 35 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11 > if (array_fact_2[mmm,nnn] = 0) then # if number 12 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 12; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 11; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 35 # Begin Function number 36 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 36 # Begin Function number 37 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 37 # Begin Function number 38 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 38 # Begin Function number 39 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 39 # Begin Function number 40 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 40 # Begin Function number 41 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 41 # Begin Function number 42 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 42 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(c(2.0) - expt(cos(c(x)),c(2))/c(2.0)); > end; exact_soln_y := proc(x) return c(2.0) - expt(cos(c(x)), c(2))/c(2.0) end proc > next_delta := proc() > global glob_nxt, x_delta; > x_delta := [ 0.001 + 0.00004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.000 + 0.000 * I ]; > glob_nxt := glob_nxt + 1; > it := x_delta[glob_nxt]; > return it; > end; Warning, `it` is implicitly declared local to procedure `next_delta` next_delta := proc() local it; global glob_nxt, x_delta; x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 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0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it end proc #END USER DEF BLOCK #END BLOCK 3 #END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I )); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and > (float_abs(rad_given) > 0.0)) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1] - array_given_rad_poles[1, 2]*I); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_complex(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if float_abs(rad_given) < float_abs(glob_least_given_sing) and 0. < float_abs(rad_given) then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_complex(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_complex(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_complex(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 3; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; > #TOP DISPLAY ALOT > ind_var := array_x[1]; > omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > omniout_complex(ALWAYS,"h ",33,glob_h,20," "); > omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > closed_form_val_y := evalf(exact_soln_y(ind_var)); > omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," "); > abserr := float_abs(numeric_val - closed_form_val_y); > if (float_abs(closed_form_val_y) > 0.0) then # if number 3 > relerr := abserr/float_abs(closed_form_val_y); > if (float_abs(c(relerr)) > 0.0) then # if number 4 > glob_good_digits := round(-log10(relerr)); > else > relerr := 0.0 ; > glob_good_digits := Digits - 2; > fi;# end if 4; > else > ; > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 3; > if (glob_good_digits < glob_min_good_digits) then # if number 3 > glob_min_good_digits := glob_good_digits; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,4," "); > omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > #BOTTOM DISPLAY ALOT > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ind_var := array_x[1]; omniout_complex(ALWAYS, "x[1] ", 33, ind_var, 20, " "); term_no := 1; numeric_val := array_y[term_no]; omniout_complex(ALWAYS, "h ", 33, glob_h, 20, " "); omniout_complex(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); closed_form_val_y := evalf(exact_soln_y(ind_var)); omniout_complex(ALWAYS, "y[1] (closed_form) ", 33, closed_form_val_y, 20, " "); abserr := float_abs(numeric_val - closed_form_val_y); if 0. < float_abs(closed_form_val_y) then relerr := abserr/float_abs(closed_form_val_y); if 0. < float_abs(c(relerr)) then glob_good_digits := round(-log10(relerr)) else relerr := 0.; glob_good_digits := Digits - 2 end if else relerr := glob__m1; glob_good_digits := -16 end if; if glob_good_digits < glob_min_good_digits then glob_min_good_digits := glob_good_digits end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 4, " "); omniout_float(ALWAYS, "relative error ", 4, relerr*glob__100, 4, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " ") end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > if (c(percent_done) < glob__100) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 3; > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > ; > if (true) then # if number 9 > display_poles(); > fi;# end if 9 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; display_poles() end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre cos 1 $eq_no = 1 > array_tmp2[1] := cos(array_x[1]); > array_tmp2_g[1] := sin(array_x[1]); > # emit pre mult FULL FULL $eq_no = 1 i = 1 > array_tmp3[1] := (array_tmp1[1] * (array_tmp2[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp1[2] := array_tmp1_g[1] * array_x[2] / c(1); > array_tmp1_g[2] := neg(array_tmp1[1]) * array_x[2] / c(1); > #emit pre cos ID_LINEAR iii = 2 $eq_no = 1 > array_tmp2[2] := neg(array_tmp2_g[1]) * array_x[2] / c(1); > array_tmp2_g[2] := array_tmp2[1] * array_x[2] / c(1); > # emit pre mult FULL FULL $eq_no = 1 i = 2 > array_tmp3[2] := ats(2,array_tmp1,array_tmp2,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := array_tmp1_g[2] * array_x[2] / c(2); > array_tmp1_g[3] := neg(array_tmp1[2]) * array_x[2] / c(2); > #emit pre cos ID_LINEAR iii = 3 $eq_no = 1 > array_tmp2[3] := neg(array_tmp2_g[2]) * array_x[2] / c(2); > array_tmp2_g[3] := array_tmp2[2] * array_x[2] / c(2); > # emit pre mult FULL FULL $eq_no = 1 i = 3 > array_tmp3[3] := ats(3,array_tmp1,array_tmp2,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp3[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := array_tmp1_g[3] * array_x[2] / c(3); > array_tmp1_g[4] := neg(array_tmp1[3]) * array_x[2] / c(3); > #emit pre cos ID_LINEAR iii = 4 $eq_no = 1 > array_tmp2[4] := neg(array_tmp2_g[3]) * array_x[2] / c(3); > array_tmp2_g[4] := array_tmp2[3] * array_x[2] / c(3); > # emit pre mult FULL FULL $eq_no = 1 i = 4 > array_tmp3[4] := ats(4,array_tmp1,array_tmp2,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp3[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := array_tmp1_g[4] * array_x[2] / c(4); > array_tmp1_g[5] := neg(array_tmp1[4]) * array_x[2] / c(4); > #emit pre cos ID_LINEAR iii = 5 $eq_no = 1 > array_tmp2[5] := neg(array_tmp2_g[4]) * array_x[2] / c(4); > array_tmp2_g[5] := array_tmp2[4] * array_x[2] / c(4); > # emit pre mult FULL FULL $eq_no = 1 i = 5 > array_tmp3[5] := ats(5,array_tmp1,array_tmp2,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp3[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sin LINEAR $eq_no = 1 > array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / c(kkk - 1); > array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1]) * array_x[2] / c(kkk - 1); > #emit cos LINEAR $eq_no = 1 > array_tmp2[kkk] := neg(array_tmp2_g[kkk - 1]) * array_x[2] / c(kkk - 1); > array_tmp2_g[kkk] := array_tmp2[kkk - 1] * array_x[2] / c(kkk - 1); > #emit mult FULL FULL $eq_no = 1 > array_tmp3[kkk] := ats(kkk,array_tmp1,array_tmp2,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp4[kkk] := array_tmp3[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp4[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := cos(array_x[1]); array_tmp2_g[1] := sin(array_x[1]); array_tmp3[1] := array_tmp1[1]*array_tmp2[1]; array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp4[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_tmp1_g[1]*array_x[2]/c(1); array_tmp1_g[2] := neg(array_tmp1[1])*array_x[2]/c(1); array_tmp2[2] := neg(array_tmp2_g[1])*array_x[2]/c(1); array_tmp2_g[2] := array_tmp2[1]*array_x[2]/c(1); array_tmp3[2] := ats(2, array_tmp1, array_tmp2, 1); array_tmp4[2] := array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp4[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp1[3] := array_tmp1_g[2]*array_x[2]/c(2); array_tmp1_g[3] := neg(array_tmp1[2])*array_x[2]/c(2); array_tmp2[3] := neg(array_tmp2_g[2])*array_x[2]/c(2); array_tmp2_g[3] := array_tmp2[2]*array_x[2]/c(2); array_tmp3[3] := ats(3, array_tmp1, array_tmp2, 1); array_tmp4[3] := array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp4[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp1[4] := array_tmp1_g[3]*array_x[2]/c(3); array_tmp1_g[4] := neg(array_tmp1[3])*array_x[2]/c(3); array_tmp2[4] := neg(array_tmp2_g[3])*array_x[2]/c(3); array_tmp2_g[4] := array_tmp2[3]*array_x[2]/c(3); array_tmp3[4] := ats(4, array_tmp1, array_tmp2, 1); array_tmp4[4] := array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp4[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp1[5] := array_tmp1_g[4]*array_x[2]/c(4); array_tmp1_g[5] := neg(array_tmp1[4])*array_x[2]/c(4); array_tmp2[5] := neg(array_tmp2_g[4])*array_x[2]/c(4); array_tmp2_g[5] := array_tmp2[4]*array_x[2]/c(4); array_tmp3[5] := ats(5, array_tmp1, array_tmp2, 1); array_tmp4[5] := array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp4[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/c(kkk - 1); array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1])*array_x[2]/c(kkk - 1) ; array_tmp2[kkk] := neg(array_tmp2_g[kkk - 1])*array_x[2]/c(kkk - 1) ; array_tmp2_g[kkk] := array_tmp2[kkk - 1]*array_x[2]/c(kkk - 1); array_tmp3[kkk] := ats(kkk, array_tmp1, array_tmp2, 1); array_tmp4[kkk] := array_tmp3[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y_set_initial[1, kkk + order_d] then temporary := c(array_tmp4[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 30; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(30),[]); > array_norms:= Array(0..(30),[]); > array_fact_1:= Array(0..(30),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(30),[]); > array_x:= Array(0..(30),[]); > array_tmp0:= Array(0..(30),[]); > array_tmp1_g:= Array(0..(30),[]); > array_tmp1:= Array(0..(30),[]); > array_tmp2_g:= Array(0..(30),[]); > array_tmp2:= Array(0..(30),[]); > array_tmp3:= Array(0..(30),[]); > array_tmp4:= Array(0..(30),[]); > array_m1:= Array(0..(30),[]); > array_y_higher := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(30) ,(0..30+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 30) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp1_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp2_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=30) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1_g); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2_g); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_h := 0.1; > glob_nxt := 1; > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 10000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 30; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 10000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/mult2postcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) * cos ( x ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1 + 0.1 * I;"); > omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_min_h := c(0.00000000001);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 3;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=10000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(c(2.0) - expt(cos(c(x)),c(2))/c(2.0));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"next_delta := proc()"); > omniout_str(ALWAYS,"global glob_nxt, x_delta;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.000 + 0.000 * I ];"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;"); > omniout_str(ALWAYS,"it := x_delta[glob_nxt];"); > omniout_str(ALWAYS,"return it;"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1 + 0.1 * I; > x_end := 99.0 + 99.0 * I; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_min_h := c(0.00000000001); > glob_type_given_pole := 3; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=10000; > glob_upper_ratio_limit:=c(1.000001); > glob_lower_ratio_limit:=c(0.999999); > glob_look_poles:=true; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > found_h := true; > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1 > #left paren 0001C > if (true) then # if number 10 > omniout_str(INFO," "); > fi;# end if 10; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > atomall(); > if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10 > display_alot(current_iter); > fi;# end if 10; > if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (true) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sin ( x ) * cos ( x ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2017-11-26T16:18:28-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mult2") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) * cos ( x ) ; ") > ; > logitem_complex(html_log_file,x_start) > ; > logitem_complex(html_log_file,x_end) > ; > logitem_complex(html_log_file,array_x[1]) > ; > logitem_complex(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > glob_desired_digits_correct := 0.0; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 11 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_min_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logitem_integer(html_log_file,ATS_MAX_TERMS) > ; > if (glob_type_given_pole = 0) then # if number 11 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 12 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 13 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 14 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 15 > logitem_str(html_log_file,"Real Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > elif > (glob_type_given_pole = 2) then # if number 16 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 16; > if (glob_least_ratio_sing < glob_large_float) then # if number 16 > glob_least_ratio_sing := 0; > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_3_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_6_sing < glob_large_float) then # if number 16 > glob_least_6_sing := 0.0; > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,(glob_clock_sec)) > ; > if (c(glob_percent_done) < glob__100) then # if number 16 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 16; > log_revs(html_log_file," 309 ") > ; > logitem_str(html_log_file,"mult2 diffeq.mxt") > ; > logitem_str(html_log_file,"mult2 maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > end; > # End Function number 12 > #END OUTFILEMAIN > end; Warning, `h_new` is implicitly declared local to procedure `main` Warning, `ratio` is implicitly declared local to procedure `main` main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new, ratio; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 30; Digits := 32; max_terms := 30; glob_html_log := true; array_y_init := Array(0 .. 30, []); array_norms := Array(0 .. 30, []); array_fact_1 := Array(0 .. 30, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 30, []); array_x := Array(0 .. 30, []); array_tmp0 := Array(0 .. 30, []); array_tmp1_g := Array(0 .. 30, []); array_tmp1 := Array(0 .. 30, []); array_tmp2_g := Array(0 .. 30, []); array_tmp2 := Array(0 .. 30, []); array_tmp3 := Array(0 .. 30, []); array_tmp4 := Array(0 .. 30, []); array_m1 := Array(0 .. 30, []); array_y_higher := Array(0 .. 2, 0 .. 31, []); array_y_higher_work := Array(0 .. 2, 0 .. 31, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []); array_y_set_initial := Array(0 .. 2, 0 .. 31, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 30, 0 .. 31, []); term := 1; while term <= 30 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 30 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 30 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp1_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp2_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 30 do term := 1; while term <= 30 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1_g); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2_g); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_h := 0.1; glob_nxt := 1; glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 10000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 30; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 10000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/mult2postcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) * \ cos ( x ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1 + 0.1 * I;"); omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_min_h := c(0.00000000001);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 3;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=10000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(c(2.0) - expt(cos(c(x)),c(2))/c(2.0));") ; omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "next_delta := proc()"); omniout_str(ALWAYS, "global glob_nxt, x_delta;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * 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I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.000 + 0.000 * I ];"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;"); omniout_str(ALWAYS, "it := x_delta[glob_nxt];"); omniout_str(ALWAYS, "return it;"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := 0.1 + 0.1*I; x_end := 99.0 + 99.0*I; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_min_h := c(0.1*10^(-10)); glob_type_given_pole := 3; glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 10000; glob_upper_ratio_limit := c(1.000001); glob_lower_ratio_limit := c(0.999999); glob_look_poles := true; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; found_h := true; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius ; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and (glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do omniout_str(INFO, " "); found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); atomall(); if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then display_alot(current_iter) end if; if glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.) then check_for_pole() end if; glob_next_display := glob_next_display + glob_display_interval; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sin ( x ) \ * cos ( x ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2017-11-26T16:18:28-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mult2"); logitem_str(html_log_file, "diff ( y , x , 1 ) = si\ n ( x ) * cos ( x ) ; "); logitem_complex(html_log_file, x_start); logitem_complex(html_log_file, x_end); logitem_complex(html_log_file, array_x[1]); logitem_complex(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); glob_desired_digits_correct := 0.; logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then glob_least_ratio_sing := 0; logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then glob_least_6_sing := 0.; logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 309 "); logitem_str(html_log_file, "mult2 diffeq.mxt"); logitem_str(html_log_file, "mult2 maple results") ; logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); memory used=3.9MB, alloc=40.3MB, time=0.08 ##############ECHO OF PROBLEM################# ##############temp/mult2postcpx.cpx################# diff ( y , x , 1 ) = sin ( x ) * cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1 + 0.1 * I; x_end := 99.0 + 99.0 * I; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_min_h := c(0.00000000001); glob_type_given_pole := 3; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=10000; glob_upper_ratio_limit:=c(1.000001); glob_lower_ratio_limit:=c(0.999999); glob_look_poles:=true; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(c(2.0) - expt(cos(c(x)),c(2))/c(2.0)); end; next_delta := proc() global glob_nxt, x_delta; x_delta := [ 0.001 + 0.00004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 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0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 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0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.000 + 0.000 * I ]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 0.1 h = 0.0001 0.005 y[1] (numeric) = 1.50006666641 0.00999982222245 y[1] (closed_form) = 1.50006666641 0.00999982222245 absolute error = 0 relative error = 0 % Correct digits = 30 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1769 Order of pole (three term test) = 22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1001 0.105 h = 0.0001 0.003 y[1] (numeric) = 1.49957351323 0.0105171837498 y[1] (closed_form) = 1.49957101302 0.0105173369035 absolute error = 2.505e-06 relative error = 0.000167 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08736 Order of pole (three term test) = 22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1002 0.108 h = 0.001 0.001 y[1] (numeric) = 1.49926519819 0.0108331709786 y[1] (closed_form) = 1.49926570209 0.0108330943034 absolute error = 5.097e-07 relative error = 3.400e-05 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06976 Order of pole (three term test) = 22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1012 0.109 h = 0.001 0.003 y[1] (numeric) = 1.49925900919 0.011043314706 y[1] (closed_form) = 1.49926094374 0.0110426223331 absolute error = 2.055e-06 relative error = 0.000137 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3343 Order of pole (three term test) = 22 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=27.5MB, alloc=40.3MB, time=0.35 x[1] = 0.1022 0.112 h = 0.0001 0.004 y[1] (numeric) = 1.49903813524 0.0114617125847 y[1] (closed_form) = 1.49903710503 0.0114621585022 absolute error = 1.123e-06 relative error = 7.488e-05 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1931 Order of pole (three term test) = 21.99 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1023 0.116 h = 0.003 0.006 y[1] (numeric) = 1.4986003133 0.0118913932203 y[1] (closed_form) = 1.49859714616 0.0118901769243 absolute error = 3.393e-06 relative error = 0.0002264 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2616 Order of pole (three term test) = 21.99 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1053 0.122 h = 0.0001 0.005 y[1] (numeric) = 1.49821408193 0.0128681130358 y[1] (closed_form) = 1.49820983217 0.0128787570593 absolute error = 1.146e-05 relative error = 0.000765 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1215 Order of pole (three term test) = 21.99 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1054 0.127 h = 0.0001 0.003 y[1] (numeric) = 1.49760783577 0.0134270587237 y[1] (closed_form) = 1.49760556969 0.0134302143742 absolute error = 3.885e-06 relative error = 0.0002594 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1005 Order of pole (three term test) = 21.98 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1055 0.13 h = 0.001 0.001 y[1] (numeric) = 1.49723450082 0.0137644664337 y[1] (closed_form) = 1.49723526196 0.0137673562693 absolute error = 2.988e-06 relative error = 0.0001996 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08018 Order of pole (three term test) = 21.98 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1065 0.131 h = 0.001 0.003 y[1] (numeric) = 1.49721284462 0.0140029471425 y[1] (closed_form) = 1.49721504186 0.0140051996392 absolute error = 3.147e-06 relative error = 0.0002102 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3838 Order of pole (three term test) = 21.98 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1075 0.134 h = 0.0001 0.004 y[1] (numeric) = 1.49693276284 0.0144625703796 y[1] (closed_form) = 1.49693198241 0.0144660052791 absolute error = 3.522e-06 relative error = 0.0002353 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2214 Order of pole (three term test) = 21.98 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1076 0.138 h = 0.003 0.006 y[1] (numeric) = 1.49640796558 0.0149204545976 y[1] (closed_form) = 1.49640500942 0.0149222369679 absolute error = 3.452e-06 relative error = 0.0002307 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2996 Order of pole (three term test) = 21.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1106 0.144 h = 0.0001 0.005 y[1] (numeric) = 1.49590969845 0.016002353316 y[1] (closed_form) = 1.49590578874 0.0160161220089 absolute error = 1.431e-05 relative error = 0.0009568 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1386 Order of pole (three term test) = 21.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1107 0.149 h = 0.0001 0.003 y[1] (numeric) = 1.49519432627 0.0165969106637 y[1] (closed_form) = 1.49519232966 0.0166030915575 absolute error = 6.495e-06 relative error = 0.0004344 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1146 Order of pole (three term test) = 21.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1108 0.152 h = 0.001 0.001 y[1] (numeric) = 1.49475560533 0.0169567025869 y[1] (closed_form) = 1.49475666432 0.0169625783702 absolute error = 5.970e-06 relative error = 0.0003994 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09134 Order of pole (three term test) = 21.96 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=72.0MB, alloc=52.3MB, time=0.91 x[1] = 0.1118 0.153 h = 0.001 0.003 y[1] (numeric) = 1.49471866496 0.0172239754358 y[1] (closed_form) = 1.4947211675 0.0172291897368 absolute error = 5.784e-06 relative error = 0.0003869 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4369 Order of pole (three term test) = 21.96 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1128 0.156 h = 0.0001 0.004 y[1] (numeric) = 1.4943792934 0.0177259236524 y[1] (closed_form) = 1.49437880104 0.0177323694036 absolute error = 6.465e-06 relative error = 0.0004326 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2516 Order of pole (three term test) = 21.96 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1129 0.16 h = 0.003 0.006 y[1] (numeric) = 1.49376699092 0.0182133362423 y[1] (closed_form) = 1.49376427851 0.0182181381645 absolute error = 5.515e-06 relative error = 0.0003692 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3403 Order of pole (three term test) = 21.96 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1159 0.166 h = 0.0001 0.005 y[1] (numeric) = 1.49315678875 0.0194028520035 y[1] (closed_form) = 1.49315326132 0.0194197890026 absolute error = 1.730e-05 relative error = 0.001159 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.157 Order of pole (three term test) = 21.95 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.116 0.171 h = 0.0001 0.003 y[1] (numeric) = 1.49233154061 0.0200347728933 y[1] (closed_form) = 1.49232985209 0.020044007043 absolute error = 9.387e-06 relative error = 0.000629 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1296 Order of pole (three term test) = 21.94 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1161 0.174 h = 0.001 0.001 y[1] (numeric) = 1.49182696923 0.0204180145976 y[1] (closed_form) = 1.49182836998 0.0204269009336 absolute error = 8.996e-06 relative error = 0.000603 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1033 Order of pole (three term test) = 21.94 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1171 0.175 h = 0.001 0.003 y[1] (numeric) = 1.4917749267 0.0207146015192 y[1] (closed_form) = 1.49177778049 0.0207227996761 absolute error = 8.681e-06 relative error = 0.0005818 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4935 Order of pole (three term test) = 21.94 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1181 0.178 h = 0.0001 0.004 y[1] (numeric) = 1.49137611477 0.0212601068529 y[1] (closed_form) = 1.4913759521 0.0212695905477 absolute error = 9.485e-06 relative error = 0.0006359 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2839 Order of pole (three term test) = 21.94 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1182 0.182 h = 0.003 0.006 y[1] (numeric) = 1.49067564511 0.0217785081087 y[1] (closed_form) = 1.49067321249 0.0217863557485 absolute error = 8.216e-06 relative error = 0.0005511 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3837 Order of pole (three term test) = 21.93 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1212 0.188 h = 0.0001 0.005 y[1] (numeric) = 1.48995350492 0.0230783797744 y[1] (closed_form) = 1.48995040565 0.023098534138 absolute error = 2.039e-05 relative error = 0.001368 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1766 Order of pole (three term test) = 21.93 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1213 0.193 h = 0.0001 0.003 y[1] (numeric) = 1.48901746531 0.0237495867572 y[1] (closed_form) = 1.48901612693 0.0237619074566 absolute error = 1.239e-05 relative error = 0.0008322 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1456 Order of pole (three term test) = 21.92 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=116.8MB, alloc=52.3MB, time=1.45 x[1] = 0.1214 0.196 h = 0.001 0.001 y[1] (numeric) = 1.48844648084 0.0241574480232 y[1] (closed_form) = 1.48844827071 0.0241693746887 absolute error = 1.206e-05 relative error = 0.0008101 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.116 Order of pole (three term test) = 21.92 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1224 0.197 h = 0.0001 0.004 y[1] (numeric) = 1.48837951797 0.024483938506 y[1] (closed_form) = 1.48838277238 0.0244951476847 absolute error = 1.167e-05 relative error = 0.0007841 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7008 Order of pole (three term test) = 21.92 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1225 0.201 h = 0.003 0.006 y[1] (numeric) = 1.48760630953 0.0250287240391 y[1] (closed_form) = 1.48760306766 0.0250388040097 absolute error = 1.059e-05 relative error = 0.0007117 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4233 Order of pole (three term test) = 21.91 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1255 0.207 h = 0.0001 0.005 y[1] (numeric) = 1.48678637244 0.0264246775431 y[1] (closed_form) = 1.4867825974 0.026447232385 absolute error = 2.287e-05 relative error = 0.001538 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1945 Order of pole (three term test) = 21.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1256 0.212 h = 0.0001 0.003 y[1] (numeric) = 1.48575360543 0.0271300360601 y[1] (closed_form) = 1.48575152268 0.0271446308905 absolute error = 1.474e-05 relative error = 0.0009921 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1603 Order of pole (three term test) = 21.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1257 0.215 h = 0.001 0.001 y[1] (numeric) = 1.48512461504 0.0275593052153 y[1] (closed_form) = 1.48512569898 0.0275734638698 absolute error = 1.420e-05 relative error = 0.000956 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1276 Order of pole (three term test) = 21.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1267 0.216 h = 0.001 0.003 y[1] (numeric) = 1.4850445883 0.0279118852101 y[1] (closed_form) = 1.48504714866 0.0279252991804 absolute error = 1.366e-05 relative error = 0.0009194 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6091 Order of pole (three term test) = 21.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1277 0.219 h = 0.0001 0.004 y[1] (numeric) = 1.48453397953 0.028541468158 y[1] (closed_form) = 1.4845334711 0.0285562817656 absolute error = 1.482e-05 relative error = 0.0009983 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.35 Order of pole (three term test) = 21.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1278 0.223 h = 0.003 0.006 y[1] (numeric) = 1.48366682108 0.0291208217345 y[1] (closed_form) = 1.48366393462 0.0291340107411 absolute error = 1.350e-05 relative error = 0.0009098 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4723 Order of pole (three term test) = 21.88 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1308 0.229 h = 0.0001 0.005 y[1] (numeric) = 1.48273463176 0.0306330426744 y[1] (closed_form) = 1.4827313797 0.0306589214176 absolute error = 2.608e-05 relative error = 0.001759 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2167 Order of pole (three term test) = 21.87 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1309 0.234 h = 0.0001 0.003 y[1] (numeric) = 1.48158890162 0.0313817186719 y[1] (closed_form) = 1.48158725617 0.0313994767403 absolute error = 1.783e-05 relative error = 0.001203 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1784 Order of pole (three term test) = 21.86 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=161.5MB, alloc=52.3MB, time=1.98 x[1] = 0.131 0.237 h = 0.001 0.001 y[1] (numeric) = 1.4808921729 0.0318380612971 y[1] (closed_form) = 1.48089374312 0.0318553301596 absolute error = 1.734e-05 relative error = 0.001171 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.142 Order of pole (three term test) = 21.86 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.132 0.238 h = 0.001 0.003 y[1] (numeric) = 1.48079755775 0.0322218269522 y[1] (closed_form) = 1.48080061963 0.0322383168122 absolute error = 1.677e-05 relative error = 0.001132 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6776 Order of pole (three term test) = 21.86 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.133 0.241 h = 0.0001 0.004 y[1] (numeric) = 1.48022668633 0.0328992418604 y[1] (closed_form) = 1.48022664552 0.0329172005158 absolute error = 1.796e-05 relative error = 0.001213 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.389 Order of pole (three term test) = 21.85 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1331 0.245 h = 0.003 0.006 y[1] (numeric) = 1.47926871564 0.0335145277246 y[1] (closed_form) = 1.47926623044 0.0335308671801 absolute error = 1.653e-05 relative error = 0.001117 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5248 Order of pole (three term test) = 21.85 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1361 0.251 h = 0.0001 0.005 y[1] (numeric) = 1.47822398497 0.035146643967 y[1] (closed_form) = 1.4782213129 0.0351759115096 absolute error = 2.939e-05 relative error = 0.001988 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2404 Order of pole (three term test) = 21.84 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1362 0.256 h = 0.0001 0.003 y[1] (numeric) = 1.47696390062 0.0359410719756 y[1] (closed_form) = 1.47696274485 0.0359620418702 absolute error = 2.100e-05 relative error = 0.001422 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1979 Order of pole (three term test) = 21.83 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1363 0.259 h = 0.001 0.001 y[1] (numeric) = 1.47619858866 0.036425970475 y[1] (closed_form) = 1.47620070295 0.0364463942408 absolute error = 2.053e-05 relative error = 0.001391 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1574 Order of pole (three term test) = 21.82 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1373 0.26 h = 0.001 0.003 y[1] (numeric) = 1.47608957062 0.0368417100031 y[1] (closed_form) = 1.47609319379 0.0368613176355 absolute error = 1.994e-05 relative error = 0.00135 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.751 Order of pole (three term test) = 21.82 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1383 0.263 h = 0.0001 0.004 y[1] (numeric) = 1.47545802745 0.0375687250418 y[1] (closed_form) = 1.47545850976 0.0375898762019 absolute error = 2.116e-05 relative error = 0.001433 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.431 Order of pole (three term test) = 21.82 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1384 0.267 h = 0.003 0.006 y[1] (numeric) = 1.47440807144 0.0382219592464 y[1] (closed_form) = 1.47440603702 0.038241495935 absolute error = 1.964e-05 relative error = 0.001332 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5811 Order of pole (three term test) = 21.81 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1414 0.273 h = 0.0001 0.005 y[1] (numeric) = 1.47325041689 0.0399779223388 y[1] (closed_form) = 1.47324838606 0.0400106492181 absolute error = 3.279e-05 relative error = 0.002225 % Correct digits = 5 memory used=206.3MB, alloc=52.3MB, time=2.52 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2659 Order of pole (three term test) = 21.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1415 0.278 h = 0.0001 0.003 y[1] (numeric) = 1.47187442142 0.0408207270357 y[1] (closed_form) = 1.47187381158 0.0408449627453 absolute error = 2.424e-05 relative error = 0.001646 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2188 Order of pole (three term test) = 21.79 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1416 0.281 h = 0.001 0.001 y[1] (numeric) = 1.47103958285 0.0413357798889 y[1] (closed_form) = 1.47104230292 0.0413594084995 absolute error = 2.378e-05 relative error = 0.001616 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.174 Order of pole (three term test) = 21.79 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1426 0.282 h = 0.001 0.003 y[1] (numeric) = 1.470916351 0.0417843532572 y[1] (closed_form) = 1.47092059919 0.0418071257072 absolute error = 2.317e-05 relative error = 0.001574 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8299 Order of pole (three term test) = 21.79 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1436 0.285 h = 0.0001 0.004 y[1] (numeric) = 1.47022366262 0.0425628836715 y[1] (closed_form) = 1.47022472746 0.0425872801271 absolute error = 2.442e-05 relative error = 0.00166 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4761 Order of pole (three term test) = 21.78 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1437 0.289 h = 0.003 0.006 y[1] (numeric) = 1.46908041587 0.0432562373107 y[1] (closed_form) = 1.46907888555 0.0432790234273 absolute error = 2.284e-05 relative error = 0.001554 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6417 Order of pole (three term test) = 21.77 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1467 0.295 h = 0.0001 0.005 y[1] (numeric) = 1.4678093645 0.0451403300453 y[1] (closed_form) = 1.46780804055 0.0451765925097 absolute error = 3.629e-05 relative error = 0.002471 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2934 Order of pole (three term test) = 21.76 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1468 0.3 h = 0.0001 0.003 y[1] (numeric) = 1.46631573471 0.0460343324941 y[1] (closed_form) = 1.46631573112 0.0460618934547 absolute error = 2.756e-05 relative error = 0.001879 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2413 Order of pole (three term test) = 21.75 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1469 0.303 h = 0.001 0.001 y[1] (numeric) = 1.46541032751 0.0465812580515 y[1] (closed_form) = 1.46541371918 0.0466081467286 absolute error = 2.710e-05 relative error = 0.001848 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1918 Order of pole (three term test) = 21.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1479 0.304 h = 0.0001 0.004 y[1] (numeric) = 1.46527307566 0.0470635983739 y[1] (closed_form) = 1.46527801666 0.0470895878756 absolute error = 2.646e-05 relative error = 0.001805 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.158 Order of pole (three term test) = 21.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.148 0.308 h = 0.003 0.006 y[1] (numeric) = 1.46405240587 0.0477913368537 y[1] (closed_form) = 1.46405013788 0.047816592582 absolute error = 2.536e-05 relative error = 0.001731 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6976 Order of pole (three term test) = 21.73 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=251.0MB, alloc=52.3MB, time=3.06 x[1] = 0.151 0.314 h = 0.0001 0.005 y[1] (numeric) = 1.46268169886 0.0497880477734 y[1] (closed_form) = 1.46267981832 0.0498270483057 absolute error = 3.905e-05 relative error = 0.002668 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3188 Order of pole (three term test) = 21.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1511 0.319 h = 0.0001 0.003 y[1] (numeric) = 1.46108464677 0.0507271011866 y[1] (closed_form) = 1.4610839982 0.0507572041906 absolute error = 3.011e-05 relative error = 0.00206 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2621 Order of pole (three term test) = 21.71 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1512 0.322 h = 0.001 0.001 y[1] (numeric) = 1.46011717661 0.0513020729113 y[1] (closed_form) = 1.46011998486 0.0513314448803 absolute error = 2.951e-05 relative error = 0.00202 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2083 Order of pole (three term test) = 21.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1522 0.323 h = 0.001 0.003 y[1] (numeric) = 1.45996759775 0.0518141191302 y[1] (closed_form) = 1.45997197575 0.0518425527162 absolute error = 2.877e-05 relative error = 0.001969 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9935 Order of pole (three term test) = 21.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1532 0.326 h = 0.0001 0.004 y[1] (numeric) = 1.45915898094 0.0526933808739 y[1] (closed_form) = 1.45916008399 0.0527236035319 absolute error = 3.024e-05 relative error = 0.002071 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5696 Order of pole (three term test) = 21.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1533 0.33 h = 0.003 0.006 y[1] (numeric) = 1.45783766597 0.0534665645486 y[1] (closed_form) = 1.45783601117 0.0534951821376 absolute error = 2.867e-05 relative error = 0.001965 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7674 Order of pole (three term test) = 21.69 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1563 0.336 h = 0.0001 0.005 y[1] (numeric) = 1.45635239168 0.0556002767641 y[1] (closed_form) = 1.45635135145 0.0556429711478 absolute error = 4.271e-05 relative error = 0.00293 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3504 Order of pole (three term test) = 21.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1564 0.341 h = 0.0001 0.003 y[1] (numeric) = 1.454634015 0.0565962982487 y[1] (closed_form) = 1.45463409537 0.0566298526204 absolute error = 3.355e-05 relative error = 0.002305 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.288 Order of pole (three term test) = 21.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1565 0.344 h = 0.001 0.001 y[1] (numeric) = 1.45359374952 0.0572066582647 y[1] (closed_form) = 1.45359736253 0.0572394081535 absolute error = 3.295e-05 relative error = 0.002265 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2289 Order of pole (three term test) = 21.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1575 0.345 h = 0.001 0.003 y[1] (numeric) = 1.45343051482 0.0577544102326 y[1] (closed_form) = 1.45343572252 0.0577861729213 absolute error = 3.219e-05 relative error = 0.002213 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.092 Order of pole (three term test) = 21.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1585 0.348 h = 0.0001 0.004 y[1] (numeric) = 1.45255902211 0.058691507082 y[1] (closed_form) = 1.45256090003 0.0587251567876 absolute error = 3.370e-05 relative error = 0.002318 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6257 Order of pole (three term test) = 21.65 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=295.7MB, alloc=52.3MB, time=3.60 x[1] = 0.1586 0.352 h = 0.003 0.006 y[1] (numeric) = 1.45113991482 0.0595119045554 y[1] (closed_form) = 1.45113893822 0.0595439520026 absolute error = 3.206e-05 relative error = 0.002208 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8428 Order of pole (three term test) = 21.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1616 0.358 h = 0.0001 0.005 y[1] (numeric) = 1.44953935528 0.0617878955112 y[1] (closed_form) = 1.44953923461 0.0618343768443 absolute error = 4.648e-05 relative error = 0.003204 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3847 Order of pole (three term test) = 21.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1617 0.363 h = 0.0001 0.003 y[1] (numeric) = 1.44769744932 0.0628443050447 y[1] (closed_form) = 1.4476983314 0.0628813861664 absolute error = 3.709e-05 relative error = 0.00256 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3161 Order of pole (three term test) = 21.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1618 0.366 h = 0.001 0.001 y[1] (numeric) = 1.44658306076 0.0634921372084 y[1] (closed_form) = 1.44658755698 0.0635283356359 absolute error = 3.648e-05 relative error = 0.002519 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2512 Order of pole (three term test) = 21.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1628 0.367 h = 0.001 0.003 y[1] (numeric) = 1.44640638361 0.0640767462513 y[1] (closed_form) = 1.44641250146 0.0641119053733 absolute error = 3.569e-05 relative error = 0.002465 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.198 Order of pole (three term test) = 21.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1638 0.37 h = 0.0001 0.004 y[1] (numeric) = 1.44547129992 0.0650742005011 y[1] (closed_form) = 1.44547402884 0.0651113511332 absolute error = 3.725e-05 relative error = 0.002574 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6864 Order of pole (three term test) = 21.59 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1639 0.374 h = 0.003 0.006 y[1] (numeric) = 1.44395257758 0.0659446321964 y[1] (closed_form) = 1.4439523486 0.065980183122 absolute error = 3.555e-05 relative error = 0.00246 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9245 Order of pole (three term test) = 21.58 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1669 0.38 h = 0.0001 0.005 y[1] (numeric) = 1.4422359373 0.0683685464021 y[1] (closed_form) = 1.44223682066 0.0684189138314 absolute error = 5.038e-05 relative error = 0.003489 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4218 Order of pole (three term test) = 21.57 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.167 0.385 h = 0.0001 0.003 y[1] (numeric) = 1.44026812844 0.0694889893635 y[1] (closed_form) = 1.44026988975 0.0695296783019 absolute error = 4.073e-05 relative error = 0.002824 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3466 Order of pole (three term test) = 21.55 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1671 0.388 h = 0.001 0.001 y[1] (numeric) = 1.4390781888 0.0701765150377 y[1] (closed_form) = 1.43908365153 0.0702162380883 absolute error = 4.010e-05 relative error = 0.002783 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2754 Order of pole (three term test) = 21.54 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1681 0.389 h = 0.001 0.003 y[1] (numeric) = 1.43888829245 0.0707992122463 y[1] (closed_form) = 1.43889540573 0.0708378404773 absolute error = 3.928e-05 relative error = 0.002726 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.313 Order of pole (three term test) = 21.54 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=340.6MB, alloc=52.3MB, time=4.14 x[1] = 0.1691 0.392 h = 0.0001 0.004 y[1] (numeric) = 1.43788884305 0.0718597156091 y[1] (closed_form) = 1.43789250392 0.071900446638 absolute error = 4.090e-05 relative error = 0.002841 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7523 Order of pole (three term test) = 21.54 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1692 0.396 h = 0.003 0.006 y[1] (numeric) = 1.43626854793 0.0727831861534 y[1] (closed_form) = 1.43626914063 0.0728223198698 absolute error = 3.914e-05 relative error = 0.002721 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.013 Order of pole (three term test) = 21.52 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1722 0.402 h = 0.0001 0.005 y[1] (numeric) = 1.43443495774 0.0753610462207 y[1] (closed_form) = 1.43443693505 0.0754154050437 absolute error = 5.439e-05 relative error = 0.003787 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4621 Order of pole (three term test) = 21.51 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1723 0.407 h = 0.0001 0.003 y[1] (numeric) = 1.43233870247 0.0765494022539 y[1] (closed_form) = 1.43234142549 0.0765937858352 absolute error = 4.447e-05 relative error = 0.0031 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3796 Order of pole (three term test) = 21.49 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1724 0.41 h = 0.001 0.001 y[1] (numeric) = 1.431071683 0.0772789856917 y[1] (closed_form) = 1.43107820057 0.0773223149764 absolute error = 4.382e-05 relative error = 0.003057 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3016 Order of pole (three term test) = 21.48 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1734 0.411 h = 0.0001 0.004 y[1] (numeric) = 1.43086880215 0.0779410839581 y[1] (closed_form) = 1.43087700118 0.0779832593721 absolute error = 4.296e-05 relative error = 0.002998 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.819 Order of pole (three term test) = 21.48 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1735 0.415 h = 0.003 0.006 y[1] (numeric) = 1.42916380245 0.0789101313227 y[1] (closed_form) = 1.42916375141 0.0789520951108 absolute error = 4.196e-05 relative error = 0.002932 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.096 Order of pole (three term test) = 21.47 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1765 0.421 h = 0.0001 0.005 y[1] (numeric) = 1.42722685766 0.081624214484 y[1] (closed_form) = 1.42722843365 0.0816817797893 absolute error = 5.759e-05 relative error = 0.004028 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4996 Order of pole (three term test) = 21.46 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1766 0.426 h = 0.0001 0.003 y[1] (numeric) = 1.42501699634 0.0828727458926 y[1] (closed_form) = 1.42501920173 0.0829200637082 absolute error = 4.737e-05 relative error = 0.003318 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4104 Order of pole (three term test) = 21.44 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1767 0.429 h = 0.001 0.001 y[1] (numeric) = 1.4236817855 0.0836395929609 y[1] (closed_form) = 1.42368787149 0.0836857772208 absolute error = 4.658e-05 relative error = 0.003266 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3261 Order of pole (three term test) = 21.43 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1777 0.43 h = 0.001 0.003 y[1] (numeric) = 1.4234674337 0.0843365711105 y[1] (closed_form) = 1.42347523012 0.0843815481348 absolute error = 4.565e-05 relative error = 0.003201 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.554 Order of pole (three term test) = 21.43 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=385.3MB, alloc=52.3MB, time=4.68 x[1] = 0.1787 0.433 h = 0.0001 0.004 y[1] (numeric) = 1.42234511795 0.0855213710147 y[1] (closed_form) = 1.42234933076 0.0855686760331 absolute error = 4.749e-05 relative error = 0.003333 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8904 Order of pole (three term test) = 21.42 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1788 0.437 h = 0.003 0.006 y[1] (numeric) = 1.420529418 0.0865509217251 y[1] (closed_form) = 1.42053033842 0.0865966323219 absolute error = 4.572e-05 relative error = 0.003213 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.199 Order of pole (three term test) = 21.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1818 0.443 h = 0.0001 0.005 y[1] (numeric) = 1.41847364091 0.0894311924954 y[1] (closed_form) = 1.41847649216 0.0894929631113 absolute error = 6.184e-05 relative error = 0.004351 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5466 Order of pole (three term test) = 21.39 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1819 0.448 h = 0.0001 0.003 y[1] (numeric) = 1.41613009135 0.0907554772773 y[1] (closed_form) = 1.41613342477 0.0908066680455 absolute error = 5.130e-05 relative error = 0.003615 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.449 Order of pole (three term test) = 21.37 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.182 0.451 h = 0.001 0.001 y[1] (numeric) = 1.4147146534 0.0915691605926 y[1] (closed_form) = 1.41472197174 0.0916191190917 absolute error = 5.049e-05 relative error = 0.003562 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3567 Order of pole (three term test) = 21.36 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.183 0.452 h = 0.001 0.003 y[1] (numeric) = 1.41448777189 0.0923082112552 y[1] (closed_form) = 1.41449683533 0.0923568965402 absolute error = 4.952e-05 relative error = 0.003494 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.7 Order of pole (three term test) = 21.36 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.184 0.455 h = 0.0001 0.004 y[1] (numeric) = 1.41329851532 0.0935647366524 y[1] (closed_form) = 1.41330391915 0.0936158821105 absolute error = 5.143e-05 relative error = 0.003631 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.974 Order of pole (three term test) = 21.35 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1841 0.459 h = 0.003 0.006 y[1] (numeric) = 1.41137484552 0.0946569775498 y[1] (closed_form) = 1.41137682584 0.0947065310538 absolute error = 4.959e-05 relative error = 0.003506 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.311 Order of pole (three term test) = 21.33 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1871 0.465 h = 0.0001 0.005 y[1] (numeric) = 1.40919917424 0.0977106073074 y[1] (closed_form) = 1.40920340771 0.0977767068217 absolute error = 6.623e-05 relative error = 0.004689 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5977 Order of pole (three term test) = 21.32 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1872 0.47 h = 0.0001 0.003 y[1] (numeric) = 1.40671889784 0.0991152474797 y[1] (closed_form) = 1.40672345727 0.0991704150425 absolute error = 5.536e-05 relative error = 0.003925 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.491 Order of pole (three term test) = 21.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1873 0.473 h = 0.001 0.001 y[1] (numeric) = 1.40522141046 0.0999785717957 y[1] (closed_form) = 1.40523006524 0.10003240241 absolute error = 5.452e-05 relative error = 0.00387 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3901 Order of pole (three term test) = 21.29 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=430.1MB, alloc=52.3MB, time=5.23 x[1] = 0.1883 0.474 h = 0.001 0.003 y[1] (numeric) = 1.40498227507 0.100761254584 y[1] (closed_form) = 1.4049927116 0.100813742056 absolute error = 5.352e-05 relative error = 0.003799 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.859 Order of pole (three term test) = 21.29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1893 0.477 h = 0.0001 0.004 y[1] (numeric) = 1.4037250811 0.102092906857 y[1] (closed_form) = 1.40373177763 0.102147994583 absolute error = 5.549e-05 relative error = 0.003943 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.065 Order of pole (three term test) = 21.28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1894 0.481 h = 0.003 0.006 y[1] (numeric) = 1.40169095212 0.103251624964 y[1] (closed_form) = 1.40169408631 0.103305123494 absolute error = 5.359e-05 relative error = 0.003813 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.434 Order of pole (three term test) = 21.26 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1924 0.487 h = 0.0001 0.005 y[1] (numeric) = 1.39939426786 0.106486213138 y[1] (closed_form) = 1.39939999706 0.106556771744 absolute error = 7.079e-05 relative error = 0.005044 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6534 Order of pole (three term test) = 21.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1925 0.492 h = 0.0001 0.003 y[1] (numeric) = 1.39677405162 0.107976084852 y[1] (closed_form) = 1.39677994096 0.10803533916 absolute error = 5.955e-05 relative error = 0.00425 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5367 Order of pole (three term test) = 21.23 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1926 0.495 h = 0.001 0.001 y[1] (numeric) = 1.39519258919 0.108892022019 y[1] (closed_form) = 1.39520269054 0.10894982844 absolute error = 5.868e-05 relative error = 0.004193 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4264 Order of pole (three term test) = 21.21 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1936 0.496 h = 0.001 0.003 y[1] (numeric) = 1.39494149406 0.109719987558 y[1] (closed_form) = 1.39495341582 0.109776376795 absolute error = 5.764e-05 relative error = 0.004119 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.032 Order of pole (three term test) = 21.21 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1946 0.499 h = 0.0001 0.004 y[1] (numeric) = 1.39361531231 0.111130368501 y[1] (closed_form) = 1.39362340929 0.111189506305 absolute error = 5.969e-05 relative error = 0.004269 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.164 Order of pole (three term test) = 21.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1947 0.503 h = 0.003 0.006 y[1] (numeric) = 1.39146809541 0.112359575151 y[1] (closed_form) = 1.39147248321 0.112417126943 absolute error = 5.772e-05 relative error = 0.004135 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.567 Order of pole (three term test) = 21.18 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1977 0.509 h = 0.0001 0.005 y[1] (numeric) = 1.3890492275 0.115783164126 y[1] (closed_form) = 1.38905657285 0.115858318755 absolute error = 7.551e-05 relative error = 0.005417 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.714 Order of pole (three term test) = 21.17 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1978 0.514 h = 0.0001 0.003 y[1] (numeric) = 1.38628568274 0.117363429556 y[1] (closed_form) = 1.38629301214 0.117426886773 absolute error = 6.388e-05 relative error = 0.004591 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5865 Order of pole (three term test) = 21.15 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=474.9MB, alloc=52.3MB, time=5.77 x[1] = 0.1979 0.517 h = 0.001 0.001 y[1] (numeric) = 1.38461821557 0.118335125738 y[1] (closed_form) = 1.38462987996 0.118397017558 absolute error = 6.298e-05 relative error = 0.004532 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4659 Order of pole (three term test) = 21.13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1989 0.518 h = 0.0001 0.004 y[1] (numeric) = 1.3843554753 0.119210118402 y[1] (closed_form) = 1.38436900076 0.119270514714 absolute error = 6.189e-05 relative error = 0.004454 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.81 Order of pole (three term test) = 21.13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.199 0.522 h = 0.003 0.006 y[1] (numeric) = 1.38211360568 0.120499930091 y[1] (closed_form) = 1.38211747802 0.12056080914 absolute error = 6.100e-05 relative error = 0.004397 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.692 Order of pole (three term test) = 21.11 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.202 0.528 h = 0.0001 0.005 y[1] (numeric) = 1.37958620278 0.124091519302 y[1] (closed_form) = 1.3795933552 0.124170496525 absolute error = 7.930e-05 relative error = 0.005725 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7708 Order of pole (three term test) = 21.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2021 0.533 h = 0.0001 0.003 y[1] (numeric) = 1.37669527084 0.125752188444 y[1] (closed_form) = 1.37670225204 0.125819110551 absolute error = 6.729e-05 relative error = 0.004867 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6331 Order of pole (three term test) = 21.08 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2022 0.536 h = 0.001 0.001 y[1] (numeric) = 1.3749513497 0.126773478856 y[1] (closed_form) = 1.37496277843 0.126838730475 absolute error = 6.624e-05 relative error = 0.004798 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5029 Order of pole (three term test) = 21.06 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2032 0.537 h = 0.001 0.003 y[1] (numeric) = 1.37467826458 0.127690288261 y[1] (closed_form) = 1.37469159197 0.127753973901 absolute error = 6.507e-05 relative error = 0.004713 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.397 Order of pole (three term test) = 21.06 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2042 0.54 h = 0.0001 0.004 y[1] (numeric) = 1.37321968983 0.129256615616 y[1] (closed_form) = 1.37322902092 0.129323347787 absolute error = 6.738e-05 relative error = 0.004885 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.373 Order of pole (three term test) = 21.05 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2043 0.544 h = 0.003 0.006 y[1] (numeric) = 1.37085360057 0.130627043047 y[1] (closed_form) = 1.37085892707 0.130692194773 absolute error = 6.537e-05 relative error = 0.004747 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.848 Order of pole (three term test) = 21.03 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2073 0.55 h = 0.0001 0.005 y[1] (numeric) = 1.36820160732 0.134423816486 y[1] (closed_form) = 1.36821061764 0.134507664578 absolute error = 8.433e-05 relative error = 0.006134 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.842 Order of pole (three term test) = 21.02 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2074 0.555 h = 0.0001 0.003 y[1] (numeric) = 1.36516049881 0.136185244442 y[1] (closed_form) = 1.36516914115 0.136256604027 absolute error = 7.188e-05 relative error = 0.005239 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6916 Order of pole (three term test) = 20.99 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=519.8MB, alloc=52.3MB, time=6.31 x[1] = 0.2075 0.558 h = 0.001 0.001 y[1] (numeric) = 1.36332647378 0.137268611403 y[1] (closed_form) = 1.36333969881 0.137338169952 absolute error = 7.080e-05 relative error = 0.005167 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5494 Order of pole (three term test) = 20.98 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2085 0.559 h = 0.001 0.003 y[1] (numeric) = 1.36304236741 0.138235957752 y[1] (closed_form) = 1.36305753553 0.138303863562 absolute error = 6.958e-05 relative error = 0.005079 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.618 Order of pole (three term test) = 20.98 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2095 0.562 h = 0.0001 0.004 y[1] (numeric) = 1.36151146457 0.139892479202 y[1] (closed_form) = 1.36152253884 0.139963605352 absolute error = 7.198e-05 relative error = 0.005259 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.499 Order of pole (three term test) = 20.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2096 0.566 h = 0.003 0.006 y[1] (numeric) = 1.35902392994 0.141346162139 y[1] (closed_form) = 1.35903082844 0.141415712957 absolute error = 6.989e-05 relative error = 0.005115 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.019 Order of pole (three term test) = 20.95 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2126 0.572 h = 0.0001 0.005 y[1] (numeric) = 1.35624605222 0.145357519062 y[1] (closed_form) = 1.35625706245 0.1454463951 absolute error = 8.956e-05 relative error = 0.006565 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9197 Order of pole (three term test) = 20.94 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2127 0.577 h = 0.0001 0.003 y[1] (numeric) = 1.3530508642 0.14722575601 y[1] (closed_form) = 1.35306129736 0.147301687718 absolute error = 7.665e-05 relative error = 0.005631 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7553 Order of pole (three term test) = 20.91 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2128 0.58 h = 0.001 0.001 y[1] (numeric) = 1.35112440116 0.148374886712 y[1] (closed_form) = 1.35113955887 0.148448879275 absolute error = 7.553e-05 relative error = 0.005557 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6001 Order of pole (three term test) = 20.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2138 0.581 h = 0.001 0.003 y[1] (numeric) = 1.350829658 0.149394799389 y[1] (closed_form) = 1.35084680522 0.149467047626 absolute error = 7.426e-05 relative error = 0.005464 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.86 Order of pole (three term test) = 20.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2148 0.584 h = 0.0001 0.004 y[1] (numeric) = 1.34922518061 0.151145964632 y[1] (closed_form) = 1.34923813196 0.151221616712 absolute error = 7.675e-05 relative error = 0.005653 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.638 Order of pole (three term test) = 20.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2149 0.588 h = 0.003 0.006 y[1] (numeric) = 1.34661302014 0.152687875444 y[1] (closed_form) = 1.34662161546 0.152761958329 absolute error = 7.458e-05 relative error = 0.005503 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.205 Order of pole (three term test) = 20.86 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2179 0.594 h = 0.0001 0.005 y[1] (numeric) = 1.34370793447 0.156923723935 y[1] (closed_form) = 1.34372109496 0.157017792303 absolute error = 9.498e-05 relative error = 0.007021 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.004 Order of pole (three term test) = 20.85 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=564.7MB, alloc=52.3MB, time=6.84 x[1] = 0.218 0.599 h = 0.0001 0.003 y[1] (numeric) = 1.34035458262 0.158905158627 y[1] (closed_form) = 1.34036694383 0.158985803771 absolute error = 8.159e-05 relative error = 0.006045 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8249 Order of pole (three term test) = 20.82 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2181 0.602 h = 0.001 0.001 y[1] (numeric) = 1.33833324025 0.160123946456 y[1] (closed_form) = 1.33835047465 0.160202506402 absolute error = 8.043e-05 relative error = 0.005967 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6553 Order of pole (three term test) = 20.81 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2191 0.603 h = 0.001 0.003 y[1] (numeric) = 1.33802827439 0.161198560644 y[1] (closed_form) = 1.33804754674 0.161275279639 absolute error = 7.910e-05 relative error = 0.005869 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.123 Order of pole (three term test) = 20.81 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2201 0.606 h = 0.0001 0.004 y[1] (numeric) = 1.33634893011 0.163049060645 y[1] (closed_form) = 1.33636390011 0.163129377108 absolute error = 8.170e-05 relative error = 0.006069 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.789 Order of pole (three term test) = 20.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2202 0.61 h = 0.003 0.006 y[1] (numeric) = 1.33360881836 0.164684448902 y[1] (closed_form) = 1.33361924265 0.16476320351 absolute error = 7.944e-05 relative error = 0.005912 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.408 Order of pole (three term test) = 20.78 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2232 0.616 h = 0.0001 0.005 y[1] (numeric) = 1.33057517871 0.169155225178 y[1] (closed_form) = 1.33059064858 0.169254657723 absolute error = 0.0001006 relative error = 0.007502 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.097 Order of pole (three term test) = 20.77 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2233 0.621 h = 0.0001 0.003 y[1] (numeric) = 1.32705939589 0.1712566004 y[1] (closed_form) = 1.32707383029 0.171342107091 absolute error = 8.672e-05 relative error = 0.006481 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9009 Order of pole (three term test) = 20.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2234 0.624 h = 0.001 0.001 y[1] (numeric) = 1.3249406248 0.172549154318 y[1] (closed_form) = 1.32496008798 0.172632421406 absolute error = 8.551e-05 relative error = 0.0064 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7157 Order of pole (three term test) = 20.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2244 0.625 h = 0.0001 0.004 y[1] (numeric) = 1.32462588274 0.173680714504 y[1] (closed_form) = 1.32464743429 0.173762038757 absolute error = 8.413e-05 relative error = 0.006297 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.315 Order of pole (three term test) = 20.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2245 0.629 h = 0.003 0.006 y[1] (numeric) = 1.32177840305 0.175396441855 y[1] (closed_form) = 1.32178849098 0.175479176345 absolute error = 8.335e-05 relative error = 0.006251 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.598 Order of pole (three term test) = 20.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2275 0.635 h = 0.0001 0.005 y[1] (numeric) = 1.31863004084 0.180076657931 y[1] (closed_form) = 1.31864560185 0.180180698985 absolute error = 0.0001052 relative error = 0.007904 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.183 Order of pole (three term test) = 20.69 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=609.6MB, alloc=52.3MB, time=7.40 x[1] = 0.2276 0.64 h = 0.0001 0.003 y[1] (numeric) = 1.31496934018 0.182284948218 y[1] (closed_form) = 1.31498365691 0.182374608177 absolute error = 9.080e-05 relative error = 0.006839 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.972 Order of pole (three term test) = 20.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2277 0.643 h = 0.001 0.001 y[1] (numeric) = 1.3127636316 0.18364325581 y[1] (closed_form) = 1.31278311869 0.183730538217 absolute error = 8.943e-05 relative error = 0.006747 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7722 Order of pole (three term test) = 20.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2287 0.644 h = 0.001 0.003 y[1] (numeric) = 1.31244014209 0.184825608148 y[1] (closed_form) = 1.31246176387 0.184910856265 absolute error = 8.795e-05 relative error = 0.006635 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.679 Order of pole (three term test) = 20.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2297 0.647 h = 0.0001 0.004 y[1] (numeric) = 1.31061657267 0.186873369321 y[1] (closed_form) = 1.31063367935 0.186962602314 absolute error = 9.086e-05 relative error = 0.006863 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.107 Order of pole (three term test) = 20.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2298 0.651 h = 0.003 0.006 y[1] (numeric) = 1.30762774628 0.188696047371 y[1] (closed_form) = 1.30763992798 0.188783733488 absolute error = 8.853e-05 relative error = 0.006701 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.837 Order of pole (three term test) = 20.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2328 0.657 h = 0.0001 0.005 y[1] (numeric) = 1.30434815063 0.193632070169 y[1] (closed_form) = 1.30436633974 0.193741817763 absolute error = 0.0001112 relative error = 0.008436 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.292 Order of pole (three term test) = 20.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2329 0.662 h = 0.0001 0.003 y[1] (numeric) = 1.30051649603 0.195973790358 y[1] (closed_form) = 1.3005331765 0.19606860799 absolute error = 9.627e-05 relative error = 0.00732 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.061 Order of pole (three term test) = 20.58 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.233 0.665 h = 0.001 0.001 y[1] (numeric) = 1.29820826908 0.197414084362 y[1] (closed_form) = 1.29823028892 0.197506353434 absolute error = 9.486e-05 relative error = 0.007224 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8431 Order of pole (three term test) = 20.56 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.234 0.666 h = 0.001 0.003 y[1] (numeric) = 1.29787590052 0.198657869179 y[1] (closed_form) = 1.29790010925 0.198747991686 absolute error = 9.332e-05 relative error = 0.007107 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.018 Order of pole (three term test) = 20.56 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.235 0.669 h = 0.0001 0.004 y[1] (numeric) = 1.2959734661 0.200819789597 y[1] (closed_form) = 1.29599304024 0.200914122091 absolute error = 9.634e-05 relative error = 0.007346 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.301 Order of pole (three term test) = 20.56 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2351 0.673 h = 0.003 0.006 y[1] (numeric) = 1.29284628933 0.202752564368 y[1] (closed_form) = 1.29286071994 0.202845361731 absolute error = 9.391e-05 relative error = 0.007176 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.098 Order of pole (three term test) = 20.53 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=654.5MB, alloc=52.3MB, time=7.94 x[1] = 0.2381 0.679 h = 0.0001 0.005 y[1] (numeric) = 1.28943408449 0.207956456563 y[1] (closed_form) = 1.28945508836 0.208072104948 absolute error = 0.0001175 relative error = 0.008999 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.411 Order of pole (three term test) = 20.53 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2382 0.684 h = 0.0001 0.003 y[1] (numeric) = 1.28542667263 0.210439452841 y[1] (closed_form) = 1.28544588684 0.210539596575 absolute error = 0.000102 relative error = 0.007828 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.159 Order of pole (three term test) = 20.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2383 0.687 h = 0.001 0.001 y[1] (numeric) = 1.28301306138 0.2119665139 y[1] (closed_form) = 1.28303779131 0.212063928435 absolute error = 0.0001005 relative error = 0.007728 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9206 Order of pole (three term test) = 20.48 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2393 0.688 h = 0.001 0.003 y[1] (numeric) = 1.28267236813 0.213274309793 y[1] (closed_form) = 1.28269934315 0.213369459531 absolute error = 9.890e-05 relative error = 0.007606 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.387 Order of pole (three term test) = 20.48 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2403 0.691 h = 0.0001 0.004 y[1] (numeric) = 1.28068961623 0.215556107593 y[1] (closed_form) = 1.28071183262 0.215655704433 absolute error = 0.000102 relative error = 0.007857 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.512 Order of pole (three term test) = 20.48 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2404 0.695 h = 0.003 0.006 y[1] (numeric) = 1.27742018902 0.217605422083 y[1] (closed_form) = 1.27743703254 0.217703497536 absolute error = 9.951e-05 relative error = 0.007679 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.383 Order of pole (three term test) = 20.45 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2434 0.701 h = 0.0001 0.005 y[1] (numeric) = 1.27387400733 0.223089858638 y[1] (closed_form) = 1.27389802327 0.223211610201 absolute error = 0.0001241 relative error = 0.009595 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.541 Order of pole (three term test) = 20.46 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2435 0.706 h = 0.0001 0.003 y[1] (numeric) = 1.26968584615 0.225722398854 y[1] (closed_form) = 1.26970777368 0.225828044469 absolute error = 0.0001079 relative error = 0.008366 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.265 Order of pole (three term test) = 20.42 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2436 0.709 h = 0.001 0.001 y[1] (numeric) = 1.26716387342 0.22734126419 y[1] (closed_form) = 1.26719150054 0.227443989844 absolute error = 0.0001064 relative error = 0.008263 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.005 Order of pole (three term test) = 20.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2446 0.71 h = 0.001 0.003 y[1] (numeric) = 1.26681545439 0.228715774272 y[1] (closed_form) = 1.26684538479 0.228816110669 absolute error = 0.0001047 relative error = 0.008133 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.79 Order of pole (three term test) = 20.41 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2456 0.713 h = 0.0001 0.004 y[1] (numeric) = 1.26475089789 0.231123461172 y[1] (closed_form) = 1.26477594109 0.231228494337 absolute error = 0.000108 relative error = 0.008398 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.743 Order of pole (three term test) = 20.41 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=699.6MB, alloc=52.3MB, time=8.48 x[1] = 0.2457 0.717 h = 0.003 0.006 y[1] (numeric) = 1.26133516951 0.233296103661 y[1] (closed_form) = 1.26135459926 0.233399631422 absolute error = 0.0001053 relative error = 0.008212 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.693 Order of pole (three term test) = 20.38 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2487 0.723 h = 0.0001 0.005 y[1] (numeric) = 1.25765366071 0.239074396221 y[1] (closed_form) = 1.25768089723 0.239202461668 absolute error = 0.0001309 relative error = 0.01023 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.682 Order of pole (three term test) = 20.39 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2488 0.728 h = 0.0001 0.003 y[1] (numeric) = 1.25327956804 0.241865189624 y[1] (closed_form) = 1.25330439855 0.2419765204 absolute error = 0.0001141 relative error = 0.008936 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.382 Order of pole (three term test) = 20.36 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2489 0.731 h = 0.001 0.001 y[1] (numeric) = 1.25064614469 0.243581165007 y[1] (closed_form) = 1.25067686633 0.243689374416 absolute error = 0.0001125 relative error = 0.008828 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.098 Order of pole (three term test) = 20.34 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2499 0.732 h = 0.0001 0.004 y[1] (numeric) = 1.25029064695 0.245025221274 y[1] (closed_form) = 1.25032373202 0.245130910461 absolute error = 0.0001107 relative error = 0.008692 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.618 Order of pole (three term test) = 20.35 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.25 0.736 h = 0.003 0.006 y[1] (numeric) = 1.24675195153 0.247303777 y[1] (closed_form) = 1.24677129696 0.247412117035 absolute error = 0.0001101 relative error = 0.008658 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.985 Order of pole (three term test) = 20.32 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.253 0.742 h = 0.0001 0.005 y[1] (numeric) = 1.2429491685 0.253344542161 y[1] (closed_form) = 1.2429768855 0.253478199627 absolute error = 0.0001365 relative error = 0.01076 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.815 Order of pole (three term test) = 20.34 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2531 0.747 h = 0.0001 0.003 y[1] (numeric) = 1.23840870139 0.256276578649 y[1] (closed_form) = 1.23843373098 0.256392933539 absolute error = 0.000119 relative error = 0.009411 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.491 Order of pole (three term test) = 20.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2532 0.75 h = 0.001 0.001 y[1] (numeric) = 1.23567553731 0.258079226355 y[1] (closed_form) = 1.23570663175 0.258192279983 absolute error = 0.0001173 relative error = 0.009288 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.184 Order of pole (three term test) = 20.28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2542 0.751 h = 0.001 0.003 y[1] (numeric) = 1.23531362737 0.259585442352 y[1] (closed_form) = 1.23534714025 0.259695858342 absolute error = 0.0001154 relative error = 0.009141 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.643 Order of pole (three term test) = 20.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2552 0.754 h = 0.0001 0.004 y[1] (numeric) = 1.23309110393 0.262243419585 y[1] (closed_form) = 1.23311947499 0.262359030649 absolute error = 0.000119 relative error = 0.009442 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.232 Order of pole (three term test) = 20.3 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=744.6MB, alloc=52.3MB, time=9.02 x[1] = 0.2553 0.758 h = 0.0001 0.004 y[1] (numeric) = 1.22939016426 0.26466300066 y[1] (closed_form) = 1.22941244263 0.264777139699 absolute error = 0.0001163 relative error = 0.009247 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.595 Order of pole (three term test) = 20.27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2554 0.762 h = 0.003 0.006 y[1] (numeric) = 1.22565068224 0.267099710844 y[1] (closed_form) = 1.22567296061 0.267213849883 absolute error = 0.0001163 relative error = 0.00927 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.421 Order of pole (three term test) = 20.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2584 0.768 h = 0.0001 0.005 y[1] (numeric) = 1.22167372408 0.273512627891 y[1] (closed_form) = 1.22170516895 0.273653209263 absolute error = 0.0001441 relative error = 0.01151 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.014 Order of pole (three term test) = 20.27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2585 0.773 h = 0.0001 0.003 y[1] (numeric) = 1.2168957976 0.276644246613 y[1] (closed_form) = 1.21692416201 0.27676670842 absolute error = 0.0001257 relative error = 0.01007 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.654 Order of pole (three term test) = 20.24 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2586 0.776 h = 0.001 0.001 y[1] (numeric) = 1.21402024899 0.278569377768 y[1] (closed_form) = 1.2140549297 0.278688283882 absolute error = 0.0001239 relative error = 0.009944 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.314 Order of pole (three term test) = 20.22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2596 0.777 h = 0.001 0.003 y[1] (numeric) = 1.21364878061 0.280163901988 y[1] (closed_form) = 1.2136859604 0.280280003434 absolute error = 0.0001219 relative error = 0.009787 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.26 Order of pole (three term test) = 20.23 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2606 0.78 h = 0.0001 0.004 y[1] (numeric) = 1.21131931643 0.282989195056 y[1] (closed_form) = 1.21135117667 0.283110826409 absolute error = 0.0001257 relative error = 0.01011 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.585 Order of pole (three term test) = 20.24 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2607 0.784 h = 0.003 0.006 y[1] (numeric) = 1.20742605344 0.285573361813 y[1] (closed_form) = 1.20745149606 0.285693538721 absolute error = 0.0001228 relative error = 0.0099 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.827 Order of pole (three term test) = 20.21 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2637 0.79 h = 0.0001 0.005 y[1] (numeric) = 1.20330911115 0.292324621541 y[1] (closed_form) = 1.20334447179 0.292472221271 absolute error = 0.0001518 relative error = 0.01226 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.199 Order of pole (three term test) = 20.24 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2638 0.795 h = 0.0001 0.003 y[1] (numeric) = 1.19832784439 0.295643544876 y[1] (closed_form) = 1.19835974393 0.29577230664 absolute error = 0.0001327 relative error = 0.01075 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.806 Order of pole (three term test) = 20.22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2639 0.798 h = 0.001 0.001 y[1] (numeric) = 1.19533047042 0.297683485708 y[1] (closed_form) = 1.19536890269 0.297808455032 absolute error = 0.0001307 relative error = 0.01061 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.435 Order of pole (three term test) = 20.2 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=789.5MB, alloc=52.3MB, time=9.56 x[1] = 0.2649 0.799 h = 0.001 0.003 y[1] (numeric) = 1.19495405832 0.299357025245 y[1] (closed_form) = 1.19499505608 0.299479037426 absolute error = 0.0001287 relative error = 0.01045 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.836 Order of pole (three term test) = 20.22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2659 0.802 h = 0.0001 0.004 y[1] (numeric) = 1.19253613434 0.302335619336 y[1] (closed_form) = 1.192571665 0.30246346763 absolute error = 0.0001327 relative error = 0.01079 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.915 Order of pole (three term test) = 20.23 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.266 0.806 h = 0.003 0.006 y[1] (numeric) = 1.18847826072 0.305074110317 y[1] (closed_form) = 1.18850708328 0.305200531264 absolute error = 0.0001297 relative error = 0.01057 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.27 Order of pole (three term test) = 20.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.269 0.812 h = 0.0001 0.005 y[1] (numeric) = 1.18422012515 0.312179867426 y[1] (closed_form) = 1.1842596609 0.312334732445 absolute error = 0.0001598 relative error = 0.01305 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.401 Order of pole (three term test) = 20.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2691 0.817 h = 0.0001 0.003 y[1] (numeric) = 1.17902952988 0.315696796514 y[1] (closed_form) = 1.17906519999 0.315832074036 absolute error = 0.0001399 relative error = 0.01146 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.972 Order of pole (three term test) = 20.22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2692 0.82 h = 0.001 0.001 y[1] (numeric) = 1.17590676724 0.317858064358 y[1] (closed_form) = 1.1759491949 0.31798929968 absolute error = 0.0001379 relative error = 0.01132 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.566 Order of pole (three term test) = 20.21 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2702 0.821 h = 0.001 0.003 y[1] (numeric) = 1.17552628645 0.319614022712 y[1] (closed_form) = 1.17557134794 0.319742140629 absolute error = 0.0001358 relative error = 0.01115 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.464 Order of pole (three term test) = 20.23 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2712 0.824 h = 0.0001 0.004 y[1] (numeric) = 1.17301827203 0.322753606444 y[1] (closed_form) = 1.17305771433 0.322887882427 absolute error = 0.0001399 relative error = 0.0115 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.274 Order of pole (three term test) = 20.24 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2713 0.828 h = 0.003 0.006 y[1] (numeric) = 1.16879094211 0.325655202565 y[1] (closed_form) = 1.16882337224 0.325788081955 absolute error = 0.0001368 relative error = 0.01127 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.755 Order of pole (three term test) = 20.22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2743 0.834 h = 0.0001 0.005 y[1] (numeric) = 1.16439047733 0.333132390049 y[1] (closed_form) = 1.16443446192 0.333294776642 absolute error = 0.0001682 relative error = 0.01389 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.621 Order of pole (three term test) = 20.28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2744 0.839 h = 0.0001 0.003 y[1] (numeric) = 1.15898436829 0.33685858248 y[1] (closed_form) = 1.15902405739 0.337000599929 absolute error = 0.0001475 relative error = 0.01222 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.153 Order of pole (three term test) = 20.26 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=834.2MB, alloc=52.3MB, time=10.10 x[1] = 0.2745 0.842 h = 0.001 0.001 y[1] (numeric) = 1.1557325382 0.339148032951 y[1] (closed_form) = 1.15577921821 0.339285744762 absolute error = 0.0001454 relative error = 0.01207 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.71 Order of pole (three term test) = 20.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2755 0.843 h = 0.001 0.003 y[1] (numeric) = 1.15534893323 0.340989967738 y[1] (closed_form) = 1.15539831731 0.341124393739 absolute error = 0.0001432 relative error = 0.01189 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.15 Order of pole (three term test) = 20.27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2765 0.846 h = 0.0001 0.004 y[1] (numeric) = 1.15274918364 0.344298607412 y[1] (closed_form) = 1.15279279194 0.344439529904 absolute error = 0.0001475 relative error = 0.01226 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.667 Order of pole (three term test) = 20.29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2766 0.85 h = 0.003 0.006 y[1] (numeric) = 1.14834739485 0.347372545186 y[1] (closed_form) = 1.14838367283 0.347512105836 absolute error = 0.0001442 relative error = 0.01202 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.284 Order of pole (three term test) = 20.28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2796 0.856 h = 0.0001 0.005 y[1] (numeric) = 1.14380355194 0.355238906273 y[1] (closed_form) = 1.14385227424 0.355409080292 absolute error = 0.000177 relative error = 0.01478 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.862 Order of pole (three term test) = 20.35 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2797 0.861 h = 0.0001 0.003 y[1] (numeric) = 1.13817554609 0.359186202395 y[1] (closed_form) = 1.1382195162 0.359335192481 absolute error = 0.0001553 relative error = 0.01301 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.351 Order of pole (three term test) = 20.33 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2798 0.864 h = 0.001 0.001 y[1] (numeric) = 1.13479085395 0.361611045325 y[1] (closed_form) = 1.13484205708 0.361755451959 absolute error = 0.0001532 relative error = 0.01286 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.867 Order of pole (three term test) = 20.33 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2808 0.865 h = 0.0001 0.004 y[1] (numeric) = 1.13440514386 0.363542673883 y[1] (closed_form) = 1.13445912315 0.363683617786 absolute error = 0.0001509 relative error = 0.01267 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.26 Order of pole (three term test) = 20.36 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2809 0.869 h = 0.003 0.006 y[1] (numeric) = 1.12985656792 0.366764460997 y[1] (closed_form) = 1.12989321198 0.366910166894 absolute error = 0.0001502 relative error = 0.01265 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.779 Order of pole (three term test) = 20.35 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2839 0.875 h = 0.0001 0.005 y[1] (numeric) = 1.12518360794 0.374978938219 y[1] (closed_form) = 1.12523348933 0.375156256441 absolute error = 0.0001842 relative error = 0.01553 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.088 Order of pole (three term test) = 20.43 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.284 0.88 h = 0.0001 0.003 y[1] (numeric) = 1.11935650074 0.379123749289 y[1] (closed_form) = 1.11940122439 0.379279148982 absolute error = 0.0001617 relative error = 0.01368 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.536 Order of pole (three term test) = 20.43 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=879.2MB, alloc=52.3MB, time=10.66 x[1] = 0.2841 0.883 h = 0.001 0.001 y[1] (numeric) = 1.11585258163 0.381669543389 y[1] (closed_form) = 1.11590475737 0.381820111456 absolute error = 0.0001594 relative error = 0.01351 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.015 Order of pole (three term test) = 20.43 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2851 0.884 h = 0.001 0.003 y[1] (numeric) = 1.11546480457 0.38368147328 y[1] (closed_form) = 1.11551982226 0.3838284201 absolute error = 0.0001569 relative error = 0.0133 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.601 Order of pole (three term test) = 20.46 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2861 0.887 h = 0.0001 0.004 y[1] (numeric) = 1.11268769113 0.387326377765 y[1] (closed_form) = 1.11273662526 0.387480495307 absolute error = 0.0001617 relative error = 0.01372 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.498 Order of pole (three term test) = 20.49 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2862 0.891 h = 0.003 0.006 y[1] (numeric) = 1.10794508586 0.390745011003 y[1] (closed_form) = 1.10798605771 0.390897839037 absolute error = 0.0001582 relative error = 0.01347 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.402 Order of pole (three term test) = 20.49 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2892 0.897 h = 0.0001 0.005 y[1] (numeric) = 1.1031268426 0.399383940224 y[1] (closed_form) = 1.10318203874 0.399569570669 absolute error = 0.0001937 relative error = 0.01651 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.372 Order of pole (three term test) = 20.59 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2893 0.902 h = 0.0001 0.003 y[1] (numeric) = 1.09706527413 0.403773451836 y[1] (closed_form) = 1.097114802 0.403936284077 absolute error = 0.0001702 relative error = 0.01456 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.769 Order of pole (three term test) = 20.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2894 0.905 h = 0.001 0.001 y[1] (numeric) = 1.09342102674 0.406469006246 y[1] (closed_form) = 1.09347826574 0.40662670043 absolute error = 0.0001678 relative error = 0.01438 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.2 Order of pole (three term test) = 20.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2904 0.906 h = 0.001 0.003 y[1] (numeric) = 1.09303320853 0.408578006737 y[1] (closed_form) = 1.09309336506 0.408731885877 absolute error = 0.0001652 relative error = 0.01416 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.48 Order of pole (three term test) = 20.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2914 0.909 h = 0.0001 0.004 y[1] (numeric) = 1.09015950619 0.412417257311 y[1] (closed_form) = 1.09021340966 0.412578697014 absolute error = 0.0001702 relative error = 0.0146 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.004 Order of pole (three term test) = 20.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2915 0.913 h = 0.003 0.006 y[1] (numeric) = 1.08522713055 0.416037302497 y[1] (closed_form) = 1.08527271011 0.416197500746 absolute error = 0.0001666 relative error = 0.01433 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.083 Order of pole (three term test) = 20.69 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2945 0.919 h = 0.0001 0.005 y[1] (numeric) = 1.08026287715 0.425120935605 y[1] (closed_form) = 1.08032372446 0.425315172905 absolute error = 0.0002035 relative error = 0.01753 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.681 Order of pole (three term test) = 20.82 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=924.1MB, alloc=52.3MB, time=11.20 x[1] = 0.2946 0.924 h = 0.0001 0.003 y[1] (numeric) = 1.07395988781 0.429768809495 y[1] (closed_form) = 1.07401452474 0.429939332627 absolute error = 0.0001791 relative error = 0.01548 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.024 Order of pole (three term test) = 20.84 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2947 0.927 h = 0.001 0.001 y[1] (numeric) = 1.07017118079 0.432622440876 y[1] (closed_form) = 1.07023379714 0.432787502952 absolute error = 0.0001765 relative error = 0.01529 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.402 Order of pole (three term test) = 20.85 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2957 0.928 h = 0.001 0.003 y[1] (numeric) = 1.06978458198 0.434832720323 y[1] (closed_form) = 1.06985019321 0.434993763878 absolute error = 0.0001739 relative error = 0.01506 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.45 Order of pole (three term test) = 20.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2967 0.931 h = 0.0001 0.004 y[1] (numeric) = 1.06681263189 0.438876000586 y[1] (closed_form) = 1.06687181622 0.43904501417 absolute error = 0.0001791 relative error = 0.01552 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.555 Order of pole (three term test) = 20.95 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2968 0.935 h = 0.003 0.006 y[1] (numeric) = 1.0616848678 0.442708662438 y[1] (closed_form) = 1.06173535024 0.442876488126 absolute error = 0.0001753 relative error = 0.01523 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.826 Order of pole (three term test) = 20.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2998 0.941 h = 0.0001 0.005 y[1] (numeric) = 1.05657402601 0.452258198631 y[1] (closed_form) = 1.0566408793 0.452461347845 absolute error = 0.0002139 relative error = 0.01861 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.02 Order of pole (three term test) = 21.12 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2999 0.946 h = 0.0001 0.003 y[1] (numeric) = 1.050022457 0.457178793015 y[1] (closed_form) = 1.05008252431 0.45735727464 absolute error = 0.0001883 relative error = 0.01644 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.302 Order of pole (three term test) = 21.15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3 0.949 h = 0.001 0.001 y[1] (numeric) = 1.04608504301 0.460199241127 y[1] (closed_form) = 1.0461533675 0.460371921292 absolute error = 0.0001857 relative error = 0.01625 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.623 Order of pole (three term test) = 21.18 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.301 0.95 h = 0.001 0.003 y[1] (numeric) = 1.04570102087 0.462515191466 y[1] (closed_form) = 1.0457724193 0.462683639508 absolute error = 0.000183 relative error = 0.016 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.5 Order of pole (three term test) = 21.23 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.302 0.953 h = 0.0001 0.004 y[1] (numeric) = 1.04262917538 0.46677264881 y[1] (closed_form) = 1.04269396878 0.466949496881 absolute error = 0.0001883 relative error = 0.01649 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.158 Order of pole (three term test) = 21.29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3021 0.957 h = 0.003 0.006 y[1] (numeric) = 1.03730024679 0.470829702141 y[1] (closed_form) = 1.03735594334 0.471005421826 absolute error = 0.0001843 relative error = 0.01618 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.637 Order of pole (three term test) = 21.33 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=969.0MB, alloc=52.3MB, time=11.74 x[1] = 0.3051 0.963 h = 0.0001 0.005 y[1] (numeric) = 1.03204240574 0.480867327132 y[1] (closed_form) = 1.03211563906 0.481079703969 absolute error = 0.0002246 relative error = 0.01973 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.389 Order of pole (three term test) = 21.51 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3052 0.968 h = 0.0001 0.003 y[1] (numeric) = 1.02523489934 0.486075729571 y[1] (closed_form) = 1.0253007357 0.486262446738 absolute error = 0.000198 relative error = 0.01745 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.605 Order of pole (three term test) = 21.56 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3053 0.971 h = 0.001 0.001 y[1] (numeric) = 1.02114441548 0.489272177178 y[1] (closed_form) = 1.02121879642 0.489452734197 absolute error = 0.0001953 relative error = 0.01724 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.864 Order of pole (three term test) = 21.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3063 0.972 h = 0.0001 0.004 y[1] (numeric) = 1.02076443059 0.491698380667 y[1] (closed_form) = 1.0208419662 0.491874481375 absolute error = 0.0001924 relative error = 0.01698 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.27 Order of pole (three term test) = 21.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3064 0.976 h = 0.003 0.006 y[1] (numeric) = 1.01526621352 0.495947774881 y[1] (closed_form) = 1.01532280961 0.496130997562 absolute error = 0.0001918 relative error = 0.01697 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.4 Order of pole (three term test) = 21.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3094 0.982 h = 0.0001 0.005 y[1] (numeric) = 1.00987546095 0.506422325262 y[1] (closed_form) = 1.00995063354 0.506643408387 absolute error = 0.0002335 relative error = 0.02067 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.736 Order of pole (three term test) = 21.92 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3095 0.987 h = 0.0001 0.003 y[1] (numeric) = 1.00283792171 0.511887955492 y[1] (closed_form) = 1.00290515401 0.512082485207 absolute error = 0.0002058 relative error = 0.01828 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.89 Order of pole (three term test) = 21.99 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3096 0.99 h = 0.001 0.001 y[1] (numeric) = 0.998609844898 0.515241708247 y[1] (closed_form) = 0.99868588162 0.515429757304 absolute error = 0.0002028 relative error = 0.01805 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.09 Order of pole (three term test) = 22.03 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3106 0.991 h = 0.001 0.003 y[1] (numeric) = 0.998233197412 0.517766707618 y[1] (closed_form) = 0.998312462415 0.517950099531 absolute error = 0.0001998 relative error = 0.01776 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.73 Order of pole (three term test) = 22.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3116 0.994 h = 0.0001 0.004 y[1] (numeric) = 0.994968290488 0.522450143465 y[1] (closed_form) = 0.995040602102 0.522642791232 absolute error = 0.0002058 relative error = 0.01831 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.433 Order of pole (three term test) = 22.19 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3117 0.998 h = 0.003 0.006 y[1] (numeric) = 0.989246096973 0.526955575362 y[1] (closed_form) = 0.989308528437 0.527147217764 absolute error = 0.0002016 relative error = 0.01798 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.35 Order of pole (three term test) = 22.26 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1013.9MB, alloc=52.3MB, time=12.29 x[1] = 0.3147 1.004 h = 0.0001 0.005 y[1] (numeric) = 0.983707801415 0.537962264547 y[1] (closed_form) = 0.983790100656 0.53819319692 absolute error = 0.0002452 relative error = 0.02186 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.171 Order of pole (three term test) = 22.51 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3148 1.009 h = 0.0001 0.003 y[1] (numeric) = 0.976399905056 0.543745744167 y[1] (closed_form) = 0.976473582155 0.54394905531 absolute error = 0.0002162 relative error = 0.01935 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.248 Order of pole (three term test) = 22.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3149 1.012 h = 0.001 0.001 y[1] (numeric) = 0.972010211868 0.547293779292 y[1] (closed_form) = 0.972092999491 0.547490214694 absolute error = 0.0002132 relative error = 0.01911 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.374 Order of pole (three term test) = 22.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3159 1.013 h = 0.001 0.003 y[1] (numeric) = 0.971640558149 0.54993810966 y[1] (closed_form) = 0.971726657827 0.550129642742 absolute error = 0.00021 relative error = 0.01881 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.08 Order of pole (three term test) = 22.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3169 1.016 h = 0.0001 0.004 y[1] (numeric) = 0.968271022673 0.554867477501 y[1] (closed_form) = 0.968349978749 0.555068760526 absolute error = 0.0002162 relative error = 0.01937 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.208 Order of pole (three term test) = 22.85 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.317 1.02 h = 0.003 0.006 y[1] (numeric) = 0.962330108055 0.559634304577 y[1] (closed_form) = 0.962398736599 0.559834661279 absolute error = 0.0002118 relative error = 0.01902 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.4 Order of pole (three term test) = 22.94 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.32 1.026 h = 0.0001 0.005 y[1] (numeric) = 0.956644438683 0.571198374749 y[1] (closed_form) = 0.956734299176 0.571439504071 absolute error = 0.0002573 relative error = 0.02309 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.647 Order of pole (three term test) = 23.24 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3201 1.031 h = 0.0001 0.003 y[1] (numeric) = 0.9490582532 0.577317070806 y[1] (closed_form) = 0.9491387682 0.577529468745 absolute error = 0.0002271 relative error = 0.02044 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.638 Order of pole (three term test) = 23.36 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3202 1.034 h = 0.001 0.001 y[1] (numeric) = 0.944502248135 0.581069955315 y[1] (closed_form) = 0.944592189961 0.581275061389 absolute error = 0.000224 relative error = 0.02019 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.685 Order of pole (three term test) = 23.44 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3212 1.035 h = 0.001 0.003 y[1] (numeric) = 0.944141381373 0.583838784446 y[1] (closed_form) = 0.944234720495 0.584038730993 absolute error = 0.0002207 relative error = 0.01987 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.56 Order of pole (three term test) = 23.52 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3222 1.038 h = 0.0001 0.004 y[1] (numeric) = 0.940665671347 0.58902621874 y[1] (closed_form) = 0.940751672723 0.589236433768 absolute error = 0.0002271 relative error = 0.02046 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.06 Order of pole (three term test) = 23.66 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1058.8MB, alloc=52.3MB, time=12.83 x[1] = 0.3223 1.042 h = 0.003 0.006 y[1] (numeric) = 0.93449964817 0.594068678316 y[1] (closed_form) = 0.934574854931 0.59427805401 absolute error = 0.0002225 relative error = 0.02009 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.54 Order of pole (three term test) = 23.77 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3253 1.048 h = 0.0001 0.005 y[1] (numeric) = 0.92866702545 0.606216525747 y[1] (closed_form) = 0.928764905099 0.606468211262 absolute error = 0.00027 relative error = 0.02435 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.166 Order of pole (three term test) = 24.11 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3254 1.053 h = 0.0001 0.003 y[1] (numeric) = 0.920794424072 0.612688676337 y[1] (closed_form) = 0.920882191027 0.612910476634 absolute error = 0.0002385 relative error = 0.02156 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.065 Order of pole (three term test) = 24.27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3255 1.056 h = 0.001 0.001 y[1] (numeric) = 0.91606729944 0.616657506042 y[1] (closed_form) = 0.916164819911 0.616871576255 absolute error = 0.0002352 relative error = 0.0213 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.023 Order of pole (three term test) = 24.36 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3265 1.057 h = 0.001 0.003 y[1] (numeric) = 0.915717145019 0.619556220569 y[1] (closed_form) = 0.915818149409 0.619764861467 absolute error = 0.0002318 relative error = 0.02096 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.17 Order of pole (three term test) = 24.46 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3275 1.06 h = 0.0001 0.004 y[1] (numeric) = 0.912133761598 0.625014425517 y[1] (closed_form) = 0.912227230295 0.625233879009 absolute error = 0.0002385 relative error = 0.02157 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.98 Order of pole (three term test) = 24.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3276 1.064 h = 0.003 0.006 y[1] (numeric) = 0.905736089029 0.630347467671 y[1] (closed_form) = 0.905818275558 0.630566177361 absolute error = 0.0002336 relative error = 0.02117 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.78 Order of pole (three term test) = 24.75 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3306 1.07 h = 0.0001 0.005 y[1] (numeric) = 0.89975721012 0.643106690472 y[1] (closed_form) = 0.899863591308 0.643369303193 absolute error = 0.0002833 relative error = 0.02561 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.733 Order of pole (three term test) = 25.15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3307 1.075 h = 0.0001 0.003 y[1] (numeric) = 0.891589873504 0.649951445586 y[1] (closed_form) = 0.891685328465 0.650182974186 absolute error = 0.0002504 relative error = 0.02269 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.53 Order of pole (three term test) = 25.34 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3308 1.078 h = 0.001 0.001 y[1] (numeric) = 0.886686711013 0.654147869818 y[1] (closed_form) = 0.886792256757 0.654371206915 absolute error = 0.000247 relative error = 0.02241 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.393 Order of pole (three term test) = 25.46 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3318 1.079 h = 0.0001 0.004 y[1] (numeric) = 0.886349335047 0.657182083269 y[1] (closed_form) = 0.886458452623 0.657399708111 absolute error = 0.0002434 relative error = 0.02206 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.49 Order of pole (three term test) = 25.56 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1103.8MB, alloc=52.3MB, time=13.38 x[1] = 0.3319 1.083 h = 0.003 0.006 y[1] (numeric) = 0.879756769364 0.662764010177 y[1] (closed_form) = 0.879840592805 0.662991885796 absolute error = 0.0002428 relative error = 0.02204 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.95 Order of pole (three term test) = 25.73 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3349 1.089 h = 0.0001 0.005 y[1] (numeric) = 0.873645033974 0.676070813344 y[1] (closed_form) = 0.873754410023 0.676344028879 absolute error = 0.0002943 relative error = 0.02663 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.265 Order of pole (three term test) = 26.17 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.335 1.094 h = 0.0001 0.003 y[1] (numeric) = 0.865212425401 0.683248707217 y[1] (closed_form) = 0.865310150919 0.683489758984 absolute error = 0.0002601 relative error = 0.02359 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.967 Order of pole (three term test) = 26.39 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3351 1.097 h = 0.001 0.001 y[1] (numeric) = 0.860150803136 0.687648628637 y[1] (closed_form) = 0.86025892425 0.687881076461 absolute error = 0.0002564 relative error = 0.02327 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.74 Order of pole (three term test) = 26.54 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3361 1.098 h = 0.001 0.003 y[1] (numeric) = 0.859824485561 0.690804338076 y[1] (closed_form) = 0.859936258724 0.691030820177 absolute error = 0.0002526 relative error = 0.02289 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.59 Order of pole (three term test) = 26.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3371 1.101 h = 0.0001 0.004 y[1] (numeric) = 0.856033346789 0.696800929245 y[1] (closed_form) = 0.856137199067 0.697039306087 absolute error = 0.00026 relative error = 0.02355 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.94 Order of pole (three term test) = 26.85 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3372 1.105 h = 0.003 0.006 y[1] (numeric) = 0.84918278604 0.702714098824 y[1] (closed_form) = 0.849274390272 0.702951928118 absolute error = 0.0002549 relative error = 0.02312 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.42 Order of pole (three term test) = 27.05 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3402 1.111 h = 0.0001 0.005 y[1] (numeric) = 0.842926557053 0.716687018773 y[1] (closed_form) = 0.843045396863 0.716971890479 absolute error = 0.0003087 relative error = 0.02789 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.933 Order of pole (three term test) = 27.56 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3403 1.116 h = 0.0001 0.003 y[1] (numeric) = 0.834182974175 0.724275621132 y[1] (closed_form) = 0.834289257263 0.724527041844 absolute error = 0.000273 relative error = 0.0247 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.516 Order of pole (three term test) = 27.82 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3404 1.119 h = 0.001 0.001 y[1] (numeric) = 0.828935719085 0.728926314719 y[1] (closed_form) = 0.829052755515 0.729168623914 absolute error = 0.0002691 relative error = 0.02437 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.176 Order of pole (three term test) = 27.99 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3414 1.12 h = 0.001 0.003 y[1] (numeric) = 0.828626356653 0.732228630116 y[1] (closed_form) = 0.828747135331 0.732464664573 absolute error = 0.0002651 relative error = 0.02397 % Correct digits = 4 memory used=1148.7MB, alloc=52.3MB, time=13.92 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.67 Order of pole (three term test) = 28.11 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3424 1.123 h = 0.0001 0.004 y[1] (numeric) = 0.824723425051 0.73853569101 y[1] (closed_form) = 0.824836074541 0.738784244125 absolute error = 0.0002729 relative error = 0.02464 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.13 Order of pole (three term test) = 28.35 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3425 1.127 h = 0.003 0.006 y[1] (numeric) = 0.817621466366 0.744786368924 y[1] (closed_form) = 0.817721317044 0.745034497782 absolute error = 0.0002675 relative error = 0.02418 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.02 Order of pole (three term test) = 28.59 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3455 1.133 h = 0.0001 0.005 y[1] (numeric) = 0.811222371293 0.759456727675 y[1] (closed_form) = 0.811351234087 0.759753661824 absolute error = 0.0003237 relative error = 0.02912 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.662 Order of pole (three term test) = 29.15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3456 1.138 h = 0.0001 0.003 y[1] (numeric) = 0.802158947973 0.767478037444 y[1] (closed_form) = 0.802274293741 0.76774018408 absolute error = 0.0002864 relative error = 0.02579 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.115 Order of pole (three term test) = 29.47 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3457 1.141 h = 0.001 0.001 y[1] (numeric) = 0.796720829366 0.772392881469 y[1] (closed_form) = 0.796847297331 0.772645382362 absolute error = 0.0002824 relative error = 0.02544 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.652 Order of pole (three term test) = 29.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3467 1.142 h = 0.001 0.003 y[1] (numeric) = 0.796430939185 0.775848114395 y[1] (closed_form) = 0.796561240567 0.776094016599 absolute error = 0.0002783 relative error = 0.02502 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.93 Order of pole (three term test) = 29.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3477 1.145 h = 0.0001 0.004 y[1] (numeric) = 0.792414981427 0.782480789874 y[1] (closed_form) = 0.792536942172 0.782739865071 absolute error = 0.0002863 relative error = 0.02571 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.42 Order of pole (three term test) = 30.07 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3478 1.149 h = 0.003 0.006 y[1] (numeric) = 0.785054504341 0.789087003109 y[1] (closed_form) = 0.785163091769 0.789345788507 absolute error = 0.0002806 relative error = 0.02521 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.77 Order of pole (three term test) = 30.34 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3508 1.155 h = 0.0001 0.005 y[1] (numeric) = 0.778514560898 0.804487528006 y[1] (closed_form) = 0.778654035433 0.804796943519 absolute error = 0.0003394 relative error = 0.03031 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.459 Order of pole (three term test) = 30.98 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3509 1.16 h = 0.0001 0.003 y[1] (numeric) = 0.769122251411 0.81296463174 y[1] (closed_form) = 0.769247191504 0.813237872386 absolute error = 0.0003005 relative error = 0.02684 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.769 Order of pole (three term test) = 31.34 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.351 1.163 h = 0.001 0.001 y[1] (numeric) = 0.763487936964 0.818157664333 y[1] (closed_form) = 0.763624379395 0.818420697039 absolute error = 0.0002963 relative error = 0.02647 % Correct digits = 4 memory used=1193.6MB, alloc=52.3MB, time=14.46 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.172 Order of pole (three term test) = 31.57 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.352 1.164 h = 0.001 0.003 y[1] (numeric) = 0.76322021434 0.821772387088 y[1] (closed_form) = 0.76336058219 0.822028481543 absolute error = 0.000292 relative error = 0.02603 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.41 Order of pole (three term test) = 31.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.353 1.167 h = 0.0001 0.004 y[1] (numeric) = 0.759090094783 0.828746521345 y[1] (closed_form) = 0.759221907628 0.829016474937 absolute error = 0.0003004 relative error = 0.02672 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.84 Order of pole (three term test) = 32.02 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3531 1.171 h = 0.003 0.006 y[1] (numeric) = 0.751463839078 0.835727186548 y[1] (closed_form) = 0.75158167944 0.835996996749 absolute error = 0.0002944 relative error = 0.02619 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.68 Order of pole (three term test) = 32.34 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3561 1.177 h = 0.0001 0.005 y[1] (numeric) = 0.744785489401 0.851892068071 y[1] (closed_form) = 0.744936195435 0.85221439673 absolute error = 0.0003558 relative error = 0.03144 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.33 Order of pole (three term test) = 33.04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3562 1.182 h = 0.0001 0.003 y[1] (numeric) = 0.735055073481 0.860849190498 y[1] (closed_form) = 0.735190167393 0.861133904522 absolute error = 0.0003151 relative error = 0.02783 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.484 Order of pole (three term test) = 33.47 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3563 1.185 h = 0.001 0.001 y[1] (numeric) = 0.729219132612 0.866335140231 y[1] (closed_form) = 0.729366120457 0.866609054768 absolute error = 0.0003109 relative error = 0.02744 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.74 Order of pole (three term test) = 33.73 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3573 1.186 h = 0.0001 0.004 y[1] (numeric) = 0.728976462099 0.870116195314 y[1] (closed_form) = 0.729127468052 0.87038281572 absolute error = 0.0003064 relative error = 0.02699 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 40.64 Order of pole (three term test) = 33.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3574 1.19 h = 0.003 0.006 y[1] (numeric) = 0.721126739498 0.877417353361 y[1] (closed_form) = 0.72124722656 0.87769835342 absolute error = 0.0003057 relative error = 0.02691 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.47 Order of pole (three term test) = 34.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3604 1.196 h = 0.0001 0.005 y[1] (numeric) = 0.714321873063 0.894267107297 y[1] (closed_form) = 0.714476992362 0.89460232867 absolute error = 0.0003694 relative error = 0.03226 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.14 Order of pole (three term test) = 35.02 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3605 1.201 h = 0.0001 0.003 y[1] (numeric) = 0.704286781121 0.903653540092 y[1] (closed_form) = 0.70442532792 0.90394985044 absolute error = 0.0003271 relative error = 0.02854 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.154 Order of pole (three term test) = 35.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3606 1.204 h = 0.001 0.001 y[1] (numeric) = 0.69826912461 0.909401476494 y[1] (closed_form) = 0.698419919258 0.90968645842 absolute error = 0.0003224 relative error = 0.02811 % Correct digits = 4 memory used=1238.5MB, alloc=52.3MB, time=15.00 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.272 Order of pole (three term test) = 35.79 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3616 1.205 h = 0.001 0.003 y[1] (numeric) = 0.698048383564 0.91333174664 y[1] (closed_form) = 0.698203281046 0.913609115591 absolute error = 0.0003177 relative error = 0.02763 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 34.65 Order of pole (three term test) = 35.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3626 1.208 h = 0.0001 0.004 y[1] (numeric) = 0.693698653355 0.920984560387 y[1] (closed_form) = 0.693844580904 0.92127715228 absolute error = 0.000327 relative error = 0.02835 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.84 Order of pole (three term test) = 36.34 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3627 1.212 h = 0.003 0.006 y[1] (numeric) = 0.68555302561 0.928712184627 y[1] (closed_form) = 0.685683794709 0.929004932355 absolute error = 0.0003206 relative error = 0.02777 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.72 Order of pole (three term test) = 36.75 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3657 1.218 h = 0.0001 0.005 y[1] (numeric) = 0.678615101707 0.946394060152 y[1] (closed_form) = 0.678782688028 0.946743041392 absolute error = 0.0003871 relative error = 0.03323 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.17 Order of pole (three term test) = 37.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3658 1.223 h = 0.0001 0.003 y[1] (numeric) = 0.668223979338 0.956308685565 y[1] (closed_form) = 0.668373795082 0.956617213321 absolute error = 0.000343 relative error = 0.02939 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.996 Order of pole (three term test) = 38.14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3659 1.226 h = 0.001 0.001 y[1] (numeric) = 0.661994146977 0.962378826306 y[1] (closed_form) = 0.662156624295 0.962675375725 absolute error = 0.0003381 relative error = 0.02894 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.941 Order of pole (three term test) = 38.47 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3669 1.227 h = 0.001 0.003 y[1] (numeric) = 0.661804279992 0.96648895423 y[1] (closed_form) = 0.661970953878 0.966777502454 absolute error = 0.0003332 relative error = 0.02844 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 37.84 Order of pole (three term test) = 38.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3679 1.23 h = 0.0001 0.004 y[1] (numeric) = 0.657337576652 0.97453267995 y[1] (closed_form) = 0.657495058909 0.974837236464 absolute error = 0.0003429 relative error = 0.02916 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.67 Order of pole (three term test) = 39.07 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.368 1.234 h = 0.003 0.006 y[1] (numeric) = 0.648904406158 0.982694070546 y[1] (closed_form) = 0.649046054669 0.982998967881 absolute error = 0.0003362 relative error = 0.02854 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.18 Order of pole (three term test) = 39.53 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.371 1.24 h = 0.0001 0.005 y[1] (numeric) = 0.641837269759 1.00124679032 y[1] (closed_form) = 0.642018040098 1.00161000157 absolute error = 0.0004057 relative error = 0.0341 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.29 Order of pole (three term test) = 40.47 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3711 1.245 h = 0.0001 0.003 y[1] (numeric) = 0.631080416343 1.01171738687 y[1] (closed_form) = 0.63124214787 1.01203854498 absolute error = 0.0003596 relative error = 0.03015 % Correct digits = 4 memory used=1283.5MB, alloc=52.3MB, time=15.55 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.91 Order of pole (three term test) = 41.08 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3712 1.248 h = 0.001 0.001 y[1] (numeric) = 0.624632709834 1.0181266159 y[1] (closed_form) = 0.624807528577 1.01843511209 absolute error = 0.0003546 relative error = 0.02968 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.671 Order of pole (three term test) = 41.46 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3722 1.249 h = 0.001 0.003 y[1] (numeric) = 0.624477205715 1.02242427499 y[1] (closed_form) = 0.624656314947 1.02272436327 absolute error = 0.0003495 relative error = 0.02916 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 41.32 Order of pole (three term test) = 41.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3732 1.252 h = 0.0001 0.004 y[1] (numeric) = 0.61989288814 1.030877751 y[1] (closed_form) = 0.620062582219 1.03119467069 absolute error = 0.0003595 relative error = 0.02988 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.66 Order of pole (three term test) = 42.12 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3733 1.256 h = 0.003 0.006 y[1] (numeric) = 0.611164409362 1.03949566191 y[1] (closed_form) = 0.611317565842 1.0398131228 absolute error = 0.0003525 relative error = 0.02922 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.86 Order of pole (three term test) = 42.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3763 1.262 h = 0.0001 0.005 y[1] (numeric) = 0.603972482345 1.05895965744 y[1] (closed_form) = 0.604167191021 1.0593375825 absolute error = 0.0004251 relative error = 0.03486 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.51 Order of pole (three term test) = 43.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3764 1.267 h = 0.0001 0.003 y[1] (numeric) = 0.592840048995 1.07001535891 y[1] (closed_form) = 0.593014376662 1.07034957224 absolute error = 0.0003769 relative error = 0.03081 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.92 Order of pole (three term test) = 44.35 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3765 1.27 h = 0.001 0.001 y[1] (numeric) = 0.58616868907 1.07678138192 y[1] (closed_form) = 0.586356541647 1.07710221445 absolute error = 0.0003718 relative error = 0.03032 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.469 Order of pole (three term test) = 44.77 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3775 1.271 h = 0.001 0.003 y[1] (numeric) = 0.586051274276 1.08127455555 y[1] (closed_form) = 0.586243511245 1.08158655409 absolute error = 0.0003665 relative error = 0.02979 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 45.12 Order of pole (three term test) = 44.99 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3785 1.274 h = 0.0001 0.004 y[1] (numeric) = 0.581348869181 1.09015747722 y[1] (closed_form) = 0.581531466008 1.09048716978 absolute error = 0.0003769 relative error = 0.0305 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.84 Order of pole (three term test) = 45.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3786 1.278 h = 0.003 0.006 y[1] (numeric) = 0.572317203962 1.09925577058 y[1] (closed_form) = 0.572482529677 1.09958622114 absolute error = 0.0003695 relative error = 0.02981 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 34.79 Order of pole (three term test) = 46.08 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3816 1.284 h = 0.0001 0.005 y[1] (numeric) = 0.565005530903 1.11967325183 y[1] (closed_form) = 0.565214971387 1.12006638832 absolute error = 0.0004454 relative error = 0.03551 % Correct digits = 3 memory used=1328.5MB, alloc=52.3MB, time=16.09 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.85 Order of pole (three term test) = 47.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3817 1.289 h = 0.0001 0.003 y[1] (numeric) = 0.553487529683 1.1313446096 y[1] (closed_form) = 0.553675169001 1.13169231507 absolute error = 0.0003951 relative error = 0.03136 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.02 Order of pole (three term test) = 47.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3818 1.292 h = 0.001 0.001 y[1] (numeric) = 0.546586662082 1.13848599169 y[1] (closed_form) = 0.546788276187 1.13881956045 absolute error = 0.0003898 relative error = 0.03085 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.34 Order of pole (three term test) = 48.44 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3828 1.293 h = 0.0001 0.004 y[1] (numeric) = 0.546511314973 1.14318298426 y[1] (closed_form) = 0.546717407127 1.14350727277 absolute error = 0.0003842 relative error = 0.03031 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 62.34 Order of pole (three term test) = 48.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3829 1.297 h = 0.003 0.006 y[1] (numeric) = 0.53722497672 1.15269217239 y[1] (closed_form) = 0.53739431957 1.15303626319 absolute error = 0.0003835 relative error = 0.03015 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 37.54 Order of pole (three term test) = 49.32 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3859 1.303 h = 0.0001 0.005 y[1] (numeric) = 0.529802704313 1.17396426202 y[1] (closed_form) = 0.530018451059 1.17437304249 absolute error = 0.0004622 relative error = 0.03587 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.1 Order of pole (three term test) = 50.53 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.386 1.308 h = 0.0001 0.003 y[1] (numeric) = 0.517936865817 1.186186394 y[1] (closed_form) = 0.518129544849 1.18654819528 absolute error = 0.0004099 relative error = 0.03166 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.04 Order of pole (three term test) = 51.37 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3861 1.311 h = 0.001 0.001 y[1] (numeric) = 0.510828916346 1.19366359419 y[1] (closed_form) = 0.511035976886 1.19401058265 absolute error = 0.0004041 relative error = 0.03111 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.16 Order of pole (three term test) = 51.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3871 1.312 h = 0.001 0.003 y[1] (numeric) = 0.510790600126 1.19854350141 y[1] (closed_form) = 0.511002224606 1.19888080971 absolute error = 0.0003982 relative error = 0.03055 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 53.16 Order of pole (three term test) = 52.14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3881 1.315 h = 0.0001 0.004 y[1] (numeric) = 0.505862138635 1.20827961825 y[1] (closed_form) = 0.506063690323 1.20863633422 absolute error = 0.0004097 relative error = 0.03127 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.44 Order of pole (three term test) = 52.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3882 1.319 h = 0.003 0.006 y[1] (numeric) = 0.496238545316 1.2183354723 y[1] (closed_form) = 0.496421375048 1.21869338751 absolute error = 0.0004019 relative error = 0.03054 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 40.99 Order of pole (three term test) = 53.45 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3912 1.325 h = 0.0001 0.005 y[1] (numeric) = 0.48870718331 1.24064465354 y[1] (closed_form) = 0.488939242814 1.24106961944 absolute error = 0.0004842 relative error = 0.0363 % Correct digits = 3 memory used=1373.5MB, alloc=52.3MB, time=16.64 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.67 Order of pole (three term test) = 54.78 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3913 1.33 h = 0.0001 0.003 y[1] (numeric) = 0.476436450846 1.25354316622 y[1] (closed_form) = 0.476643866869 1.25391931476 absolute error = 0.0004295 relative error = 0.03202 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.33 Order of pole (three term test) = 55.71 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3914 1.333 h = 0.001 0.001 y[1] (numeric) = 0.469087676797 1.26143262265 y[1] (closed_form) = 0.469309947663 1.26179312887 absolute error = 0.0004235 relative error = 0.03146 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.18 Order of pole (three term test) = 56.29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3924 1.334 h = 0.001 0.003 y[1] (numeric) = 0.469099444991 1.26653275047 y[1] (closed_form) = 0.469326372591 1.26688309024 absolute error = 0.0004174 relative error = 0.0309 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 58.05 Order of pole (three term test) = 56.56 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3934 1.337 h = 0.0001 0.004 y[1] (numeric) = 0.464052358243 1.27675972396 y[1] (closed_form) = 0.464268985625 1.27713045707 absolute error = 0.0004294 relative error = 0.0316 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 33.24 Order of pole (three term test) = 57.22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3935 1.341 h = 0.003 0.006 y[1] (numeric) = 0.454102160195 1.28737071093 y[1] (closed_form) = 0.454299240619 1.28774291281 absolute error = 0.0004212 relative error = 0.03084 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 44.76 Order of pole (three term test) = 58.01 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3965 1.347 h = 0.0001 0.005 y[1] (numeric) = 0.446468788888 1.31076469964 y[1] (closed_form) = 0.446718077308 1.31120638957 absolute error = 0.0005072 relative error = 0.03661 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.39 Order of pole (three term test) = 59.45 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3966 1.352 h = 0.0001 0.003 y[1] (numeric) = 0.433782817935 1.32437456752 y[1] (closed_form) = 0.434005796613 1.32476553591 absolute error = 0.0004501 relative error = 0.03229 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.75 Order of pole (three term test) = 60.49 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3967 1.355 h = 0.001 0.001 y[1] (numeric) = 0.426187177808 1.33269752635 y[1] (closed_form) = 0.426425497159 1.33307198052 absolute error = 0.0004439 relative error = 0.03171 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.3 Order of pole (three term test) = 61.12 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3977 1.356 h = 0.001 0.003 y[1] (numeric) = 0.426253810725 1.33802716563 y[1] (closed_form) = 0.426496878612 1.33839094417 absolute error = 0.0004375 relative error = 0.03115 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 63.39 Order of pole (three term test) = 61.41 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3987 1.359 h = 0.0001 0.004 y[1] (numeric) = 0.421088436237 1.34876835754 y[1] (closed_form) = 0.421320976724 1.34915356189 absolute error = 0.00045 relative error = 0.03183 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 36.3 Order of pole (three term test) = 62.13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3988 1.363 h = 0.003 0.006 y[1] (numeric) = 0.410803386784 1.35996311459 y[1] (closed_form) = 0.411015521029 1.36035007816 absolute error = 0.0004413 relative error = 0.03105 % Correct digits = 4 memory used=1418.3MB, alloc=52.3MB, time=17.18 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 48.88 Order of pole (three term test) = 63.01 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4018 1.369 h = 0.0001 0.005 y[1] (numeric) = 0.403075912636 1.38449170034 y[1] (closed_form) = 0.403343393161 1.38495066736 absolute error = 0.0005312 relative error = 0.03683 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.26 Order of pole (three term test) = 64.58 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4019 1.374 h = 0.0001 0.003 y[1] (numeric) = 0.389964265099 1.39884958278 y[1] (closed_form) = 0.390203674307 1.3992558561 absolute error = 0.0004716 relative error = 0.03246 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.29 Order of pole (three term test) = 65.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.402 1.377 h = 0.001 0.001 y[1] (numeric) = 0.382115671643 1.40762831115 y[1] (closed_form) = 0.382370919924 1.40801715393 absolute error = 0.0004651 relative error = 0.03188 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.53 Order of pole (three term test) = 66.42 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.403 1.378 h = 0.001 0.003 y[1] (numeric) = 0.382242263809 1.41319712016 y[1] (closed_form) = 0.382502351127 1.41357475421 absolute error = 0.0004585 relative error = 0.03131 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 69.22 Order of pole (three term test) = 66.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.404 1.381 h = 0.0001 0.004 y[1] (numeric) = 0.376959203171 1.42447694048 y[1] (closed_form) = 0.377208536698 1.42487708171 absolute error = 0.0004715 relative error = 0.03199 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 39.64 Order of pole (three term test) = 67.53 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4041 1.385 h = 0.003 0.006 y[1] (numeric) = 0.366330989623 1.43628548191 y[1] (closed_form) = 0.366559022048 1.43668769507 absolute error = 0.0004624 relative error = 0.03118 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 53.37 Order of pole (three term test) = 68.49 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4071 1.391 h = 0.0001 0.005 y[1] (numeric) = 0.358518206143 1.46200061142 y[1] (closed_form) = 0.358804891259 1.4624774231 absolute error = 0.0005564 relative error = 0.03695 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.31 Order of pole (three term test) = 70.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4072 1.396 h = 0.0001 0.003 y[1] (numeric) = 0.344970365517 1.47714492923 y[1] (closed_form) = 0.345227117376 1.47756700513 absolute error = 0.000494 relative error = 0.03256 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.97 Order of pole (three term test) = 71.46 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4073 1.399 h = 0.001 0.001 y[1] (numeric) = 0.336862695402 1.48640276157 y[1] (closed_form) = 0.337135797361 1.48680644405 absolute error = 0.0004874 relative error = 0.03197 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.86 Order of pole (three term test) = 72.23 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4083 1.4 h = 0.003 0.006 y[1] (numeric) = 0.337054673867 1.49222077883 y[1] (closed_form) = 0.33733270373 1.49261269453 absolute error = 0.0004805 relative error = 0.0314 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 160.3 Order of pole (three term test) = 72.57 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4113 1.406 h = 0.0001 0.005 y[1] (numeric) = 0.329268158901 1.51871303291 y[1] (closed_form) = 0.329559443495 1.51925353248 absolute error = 0.000614 relative error = 0.0395 % Correct digits = 3 memory used=1463.3MB, alloc=52.3MB, time=17.72 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.81 Order of pole (three term test) = 74.39 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4114 1.411 h = 0.0001 0.003 y[1] (numeric) = 0.315435151178 1.53443287997 y[1] (closed_form) = 0.315695107136 1.53491724754 absolute error = 0.0005497 relative error = 0.03508 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.2 Order of pole (three term test) = 75.73 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4115 1.414 h = 0.001 0.001 y[1] (numeric) = 0.307158501743 1.54404110879 y[1] (closed_form) = 0.307435140949 1.54450637914 absolute error = 0.0005413 relative error = 0.03437 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.84 Order of pole (three term test) = 76.55 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4125 1.415 h = 0.001 0.003 y[1] (numeric) = 0.30740538009 1.55003476091 y[1] (closed_form) = 0.30768699236 1.55048786338 absolute error = 0.0005335 relative error = 0.03375 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 80.26 Order of pole (three term test) = 76.91 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4135 1.418 h = 0.0001 0.004 y[1] (numeric) = 0.301940867999 1.5622850617 y[1] (closed_form) = 0.302211377965 1.56276261923 absolute error = 0.0005489 relative error = 0.03448 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 45.97 Order of pole (three term test) = 77.82 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4136 1.422 h = 0.003 0.006 y[1] (numeric) = 0.29073167978 1.57521082877 y[1] (closed_form) = 0.290979303002 1.5756910651 absolute error = 0.0005403 relative error = 0.03372 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 61.89 Order of pole (three term test) = 78.95 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4166 1.428 h = 0.0001 0.005 y[1] (numeric) = 0.282830484455 1.60305440778 y[1] (closed_form) = 0.283142816207 1.6036137148 absolute error = 0.0006406 relative error = 0.03934 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.19 Order of pole (three term test) = 80.93 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4167 1.433 h = 0.0001 0.003 y[1] (numeric) = 0.268544474353 1.61963002744 y[1] (closed_form) = 0.268823432092 1.62013104069 absolute error = 0.0005734 relative error = 0.03492 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.15 Order of pole (three term test) = 82.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4168 1.436 h = 0.001 0.001 y[1] (numeric) = 0.259999011881 1.62975945765 y[1] (closed_form) = 0.260295183967 1.63024032675 absolute error = 0.0005648 relative error = 0.03421 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.39 Order of pole (three term test) = 83.31 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4178 1.437 h = 0.001 0.003 y[1] (numeric) = 0.260321520151 1.63602000475 y[1] (closed_form) = 0.260622749894 1.63648810333 absolute error = 0.0005566 relative error = 0.03359 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 87.64 Order of pole (three term test) = 83.69 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4188 1.44 h = 0.0001 0.004 y[1] (numeric) = 0.254743144239 1.64888004577 y[1] (closed_form) = 0.255033051927 1.64937382323 absolute error = 0.0005726 relative error = 0.03431 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 50.19 Order of pole (three term test) = 84.69 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4189 1.444 h = 0.003 0.006 y[1] (numeric) = 0.243169102233 1.66250780259 y[1] (closed_form) = 0.243435126602 1.66300463955 absolute error = 0.0005636 relative error = 0.03353 % Correct digits = 3 memory used=1508.2MB, alloc=52.3MB, time=18.27 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 67.58 Order of pole (three term test) = 85.93 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4219 1.45 h = 0.0001 0.005 y[1] (numeric) = 0.235212638515 1.69168861962 y[1] (closed_form) = 0.235547174877 1.69226733969 absolute error = 0.0006685 relative error = 0.03912 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.78 Order of pole (three term test) = 88.08 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.422 1.455 h = 0.0001 0.003 y[1] (numeric) = 0.220463037008 1.70916357326 y[1] (closed_form) = 0.22076203872 1.70968176261 absolute error = 0.0005983 relative error = 0.0347 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.28 Order of pole (three term test) = 89.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4221 1.458 h = 0.001 0.001 y[1] (numeric) = 0.211642627508 1.71984065301 y[1] (closed_form) = 0.211959387266 1.72033759847 absolute error = 0.0005893 relative error = 0.034 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.08 Order of pole (three term test) = 90.69 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4231 1.459 h = 0.001 0.003 y[1] (numeric) = 0.21204719552 1.72637921242 y[1] (closed_form) = 0.212369094835 1.72686275672 absolute error = 0.0005809 relative error = 0.03339 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 95.71 Order of pole (three term test) = 91.11 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4241 1.462 h = 0.0001 0.004 y[1] (numeric) = 0.20635678119 1.73987765348 y[1] (closed_form) = 0.206667142009 1.74038815788 absolute error = 0.0005974 relative error = 0.03409 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 54.81 Order of pole (three term test) = 92.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4242 1.466 h = 0.003 0.006 y[1] (numeric) = 0.194409491977 1.75424305452 y[1] (closed_form) = 0.194694932198 1.75475702698 absolute error = 0.0005879 relative error = 0.0333 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 73.79 Order of pole (three term test) = 93.56 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4272 1.472 h = 0.0001 0.005 y[1] (numeric) = 0.186410476652 1.78482175489 y[1] (closed_form) = 0.186768433689 1.78542050828 absolute error = 0.0006976 relative error = 0.03886 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 33.61 Order of pole (three term test) = 95.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4273 1.477 h = 0.0001 0.003 y[1] (numeric) = 0.17118668835 1.80324167672 y[1] (closed_form) = 0.17150682881 1.80377758521 absolute error = 0.0006242 relative error = 0.03445 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.61 Order of pole (three term test) = 97.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4274 1.48 h = 0.001 0.001 y[1] (numeric) = 0.162085207373 1.81449410952 y[1] (closed_form) = 0.162423662142 1.81500761906 absolute error = 0.000615 relative error = 0.03375 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.93 Order of pole (three term test) = 98.76 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4284 1.481 h = 0.0001 0.004 y[1] (numeric) = 0.162578674018 1.82132222906 y[1] (closed_form) = 0.162922347115 1.82182167757 absolute error = 0.0006063 relative error = 0.03315 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 132.2 Order of pole (three term test) = 99.21 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4285 1.485 h = 0.003 0.006 y[1] (numeric) = 0.150318683627 1.83631793318 y[1] (closed_form) = 0.150611814212 1.83685110872 absolute error = 0.0006084 relative error = 0.03301 % Correct digits = 3 memory used=1553.2MB, alloc=52.3MB, time=18.81 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 79.62 Order of pole (three term test) = 100.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4315 1.491 h = 0.0001 0.005 y[1] (numeric) = 0.142276476001 1.86815014455 y[1] (closed_form) = 0.142645703561 1.8687707161 absolute error = 0.0007221 relative error = 0.03853 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 36.27 Order of pole (three term test) = 103.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4316 1.496 h = 0.0001 0.003 y[1] (numeric) = 0.126624014603 1.88741583743 y[1] (closed_form) = 0.126953388291 1.88797147939 absolute error = 0.0006459 relative error = 0.03414 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.79 Order of pole (three term test) = 105.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4317 1.499 h = 0.001 0.001 y[1] (numeric) = 0.117268383276 1.89918325217 y[1] (closed_form) = 0.117616574806 1.89971546149 absolute error = 0.000636 relative error = 0.03341 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.66 Order of pole (three term test) = 106.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4327 1.5 h = 0.001 0.003 y[1] (numeric) = 0.11784053201 1.90627138 y[1] (closed_form) = 0.118194015163 1.90678893677 absolute error = 0.0006267 relative error = 0.03281 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 112.8 Order of pole (three term test) = 106.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4337 1.503 h = 0.0001 0.004 y[1] (numeric) = 0.111939391639 1.92103713413 y[1] (closed_form) = 0.112280928155 1.92158419414 absolute error = 0.0006449 relative error = 0.0335 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 64.58 Order of pole (three term test) = 108.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4338 1.507 h = 0.003 0.006 y[1] (numeric) = 0.0992654070742 1.93687118993 y[1] (closed_form) = 0.0995799735786 1.93742254478 absolute error = 0.0006348 relative error = 0.03272 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 86.95 Order of pole (three term test) = 109.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4368 1.513 h = 0.0001 0.005 y[1] (numeric) = 0.0912068430244 1.97022128834 y[1] (closed_form) = 0.0916019119397 1.97086310275 absolute error = 0.0007537 relative error = 0.0382 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 39.6 Order of pole (three term test) = 112.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4369 1.518 h = 0.0001 0.003 y[1] (numeric) = 0.0750599371885 1.99052257748 y[1] (closed_form) = 0.0754126285345 1.99109699717 absolute error = 0.0006741 relative error = 0.03383 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.53 Order of pole (three term test) = 114.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.437 1.521 h = 0.001 0.001 y[1] (numeric) = 0.0654115468384 2.00292035867 y[1] (closed_form) = 0.0657836362137 2.0034700808 absolute error = 0.0006638 relative error = 0.03312 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.84 Order of pole (three term test) = 115.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.438 1.522 h = 0.001 0.003 y[1] (numeric) = 0.0660863387041 2.01032082485 y[1] (closed_form) = 0.0664637917504 2.01085517666 absolute error = 0.0006542 relative error = 0.03252 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 123.1 Order of pole (three term test) = 116.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.439 1.525 h = 0.0001 0.004 y[1] (numeric) = 0.060080259344 2.02581419551 y[1] (closed_form) = 0.0604455626354 2.02637951043 absolute error = 0.0006731 relative error = 0.0332 % Correct digits = 3 memory used=1598.1MB, alloc=52.3MB, time=19.36 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 70.52 Order of pole (three term test) = 117.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4391 1.529 h = 0.003 0.006 y[1] (numeric) = 0.0470086296851 2.04249741103 y[1] (closed_form) = 0.0473458003228 2.04306751831 absolute error = 0.0006623 relative error = 0.03241 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 94.94 Order of pole (three term test) = 119.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4421 1.535 h = 0.0001 0.005 y[1] (numeric) = 0.0389501300698 2.07743374119 y[1] (closed_form) = 0.0393724397858 2.07809746144 absolute error = 0.0007867 relative error = 0.03785 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 43.24 Order of pole (three term test) = 122.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4422 1.54 h = 0.0001 0.003 y[1] (numeric) = 0.0222982731476 2.0988227194 y[1] (closed_form) = 0.022675541421 2.09941649642 absolute error = 0.0007035 relative error = 0.03351 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.52 Order of pole (three term test) = 124.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4423 1.543 h = 0.001 0.001 y[1] (numeric) = 0.0123510947746 2.11188248143 y[1] (closed_form) = 0.0127483535995 2.11245023284 absolute error = 0.0006929 relative error = 0.0328 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.22 Order of pole (three term test) = 126.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4433 1.544 h = 0.001 0.003 y[1] (numeric) = 0.0131366657412 2.11960815361 y[1] (closed_form) = 0.0135393557252 2.12015978389 absolute error = 0.000683 relative error = 0.03221 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 134.5 Order of pole (three term test) = 126.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4443 1.547 h = 0.0001 0.004 y[1] (numeric) = 0.0070291498452 2.13586300247 y[1] (closed_form) = 0.00741949368869 2.13644712355 absolute error = 0.0007025 relative error = 0.03288 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 77.01 Order of pole (three term test) = 128.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4444 1.551 h = 0.003 0.006 y[1] (numeric) = -0.00644839869546 2.15343800222 y[1] (closed_form) = -0.00608739698615 2.15402744817 absolute error = 0.0006912 relative error = 0.03209 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 103.7 Order of pole (three term test) = 130.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4474 1.557 h = 0.0001 0.005 y[1] (numeric) = -0.014488932813 2.19003180184 y[1] (closed_form) = -0.0140379127287 2.19071810546 absolute error = 0.0008212 relative error = 0.03749 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 47.22 Order of pole (three term test) = 133.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4475 1.562 h = 0.0001 0.003 y[1] (numeric) = -0.0316561535179 2.21256301686 y[1] (closed_form) = -0.031252986161 2.21317674321 absolute error = 0.0007343 relative error = 0.03318 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 38.79 Order of pole (three term test) = 135.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4476 1.565 h = 0.001 0.001 y[1] (numeric) = -0.0419080761727 2.22631786025 y[1] (closed_form) = -0.0414843135666 2.22690416681 absolute error = 0.0007234 relative error = 0.03248 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.81 Order of pole (three term test) = 137.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4486 1.566 h = 0.001 0.003 y[1] (numeric) = -0.0410030846482 2.23438209586 y[1] (closed_form) = -0.0405738285317 2.23495149601 absolute error = 0.0007131 relative error = 0.0319 % Correct digits = 3 memory used=1643.1MB, alloc=52.3MB, time=19.90 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 146.8 Order of pole (three term test) = 138.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4496 1.569 h = 0.0001 0.004 y[1] (numeric) = -0.0472080091083 2.25143376806 y[1] (closed_form) = -0.0467912877187 2.25203725748 absolute error = 0.0007334 relative error = 0.03256 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 84.09 Order of pole (three term test) = 139.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4497 1.573 h = 0.003 0.006 y[1] (numeric) = -0.0610996585424 2.26994518179 y[1] (closed_form) = -0.0607135373143 2.27055456567 absolute error = 0.0007214 relative error = 0.03176 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 113.2 Order of pole (three term test) = 141.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4527 1.579 h = 0.0001 0.005 y[1] (numeric) = -0.0691027467751 2.30827069475 y[1] (closed_form) = -0.0686214733195 2.30898027367 absolute error = 0.0008574 relative error = 0.03712 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 51.57 Order of pole (three term test) = 145.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4528 1.584 h = 0.0001 0.003 y[1] (numeric) = -0.0867956181002 2.33200125847 y[1] (closed_form) = -0.0863651636535 2.33263553835 absolute error = 0.0007666 relative error = 0.03284 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 42.36 Order of pole (three term test) = 148.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4529 1.587 h = 0.001 0.001 y[1] (numeric) = -0.097358148533 2.34648583582 y[1] (closed_form) = -0.0969064821616 2.34709123252 absolute error = 0.0007553 relative error = 0.03215 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 33.65 Order of pole (three term test) = 149.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4539 1.588 h = 0.0001 0.004 y[1] (numeric) = -0.0963245612811 2.35490249834 y[1] (closed_form) = -0.0958673448039 2.35549016737 absolute error = 0.0007446 relative error = 0.03158 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 202.9 Order of pole (three term test) = 150.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.454 1.592 h = 0.003 0.006 y[1] (numeric) = -0.110562418121 2.37421365051 y[1] (closed_form) = -0.110165548498 2.37484628712 absolute error = 0.0007468 relative error = 0.03141 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 122.2 Order of pole (three term test) = 152.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.457 1.598 h = 0.0001 0.005 y[1] (numeric) = -0.118538281815 2.41409239208 y[1] (closed_form) = -0.118041668843 2.41482823711 absolute error = 0.0008877 relative error = 0.03672 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 55.64 Order of pole (three term test) = 156.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4571 1.603 h = 0.0001 0.003 y[1] (numeric) = -0.136706994047 2.43889666512 y[1] (closed_form) = -0.136263849652 2.43955475839 absolute error = 0.0007934 relative error = 0.03247 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 45.7 Order of pole (three term test) = 159.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4572 1.606 h = 0.001 0.001 y[1] (numeric) = -0.14755077847 2.45403456476 y[1] (closed_form) = -0.147085863314 2.45466246482 absolute error = 0.0007813 relative error = 0.03177 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 36.31 Order of pole (three term test) = 161.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4582 1.607 h = 0.001 0.003 y[1] (numeric) = -0.146403156326 2.46276777591 y[1] (closed_form) = -0.145932637068 2.46337721201 absolute error = 0.0007699 relative error = 0.0312 % Correct digits = 4 memory used=1688.1MB, alloc=52.3MB, time=20.44 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 173 Order of pole (three term test) = 162 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4592 1.61 h = 0.0001 0.004 y[1] (numeric) = -0.152787204413 2.48140053845 y[1] (closed_form) = -0.152329567224 2.48204723528 absolute error = 0.0007922 relative error = 0.03186 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 99.07 Order of pole (three term test) = 164 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4593 1.614 h = 0.003 0.006 y[1] (numeric) = -0.167483258012 2.50177526846 y[1] (closed_form) = -0.167058705102 2.5024290096 absolute error = 0.0007795 relative error = 0.03108 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 133.4 Order of pole (three term test) = 166.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4623 1.62 h = 0.0001 0.005 y[1] (numeric) = -0.17538183506 2.54353256112 y[1] (closed_form) = -0.174851898771 2.54429302725 absolute error = 0.0009269 relative error = 0.03634 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 60.76 Order of pole (three term test) = 170.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4624 1.625 h = 0.0001 0.003 y[1] (numeric) = -0.194095641859 2.5696495551 y[1] (closed_form) = -0.193622449183 2.57032937656 absolute error = 0.0008283 relative error = 0.03213 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 49.9 Order of pole (three term test) = 173.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4625 1.628 h = 0.001 0.001 y[1] (numeric) = -0.205261082079 2.58558597112 y[1] (closed_form) = -0.204765479436 2.58623399854 absolute error = 0.0008158 relative error = 0.03145 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 39.65 Order of pole (three term test) = 175.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4635 1.629 h = 0.001 0.003 y[1] (numeric) = -0.203966448288 2.59469893609 y[1] (closed_form) = -0.203465196986 2.59532760712 absolute error = 0.000804 relative error = 0.03089 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 188.9 Order of pole (three term test) = 176.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4645 1.632 h = 0.0001 0.004 y[1] (numeric) = -0.210433594415 2.61423845375 y[1] (closed_form) = -0.209945385797 2.61490620411 absolute error = 0.0008272 relative error = 0.03153 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 108.2 Order of pole (three term test) = 178.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4646 1.636 h = 0.003 0.006 y[1] (numeric) = -0.225567020589 2.63568906736 y[1] (closed_form) = -0.22511330362 2.63636454972 absolute error = 0.0008137 relative error = 0.03075 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 145.7 Order of pole (three term test) = 181.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4676 1.642 h = 0.0001 0.005 y[1] (numeric) = -0.233363753726 2.67940843996 y[1] (closed_form) = -0.232798721562 2.68019426018 absolute error = 0.0009679 relative error = 0.03598 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 66.34 Order of pole (three term test) = 185.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4677 1.647 h = 0.0001 0.003 y[1] (numeric) = -0.252632416831 2.70690324978 y[1] (closed_form) = -0.252127582056 2.70760543828 absolute error = 0.0008648 relative error = 0.0318 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 54.49 Order of pole (three term test) = 189.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4678 1.65 h = 0.001 0.001 y[1] (numeric) = -0.264125006868 2.723677666 y[1] (closed_form) = -0.263597111715 2.72434638074 absolute error = 0.000852 relative error = 0.03113 % Correct digits = 4 memory used=1733.3MB, alloc=52.3MB, time=20.99 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 43.29 Order of pole (three term test) = 191.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4688 1.651 h = 0.001 0.003 y[1] (numeric) = -0.262672497062 2.73318579742 y[1] (closed_form) = -0.26213891645 2.73383422278 absolute error = 0.0008397 relative error = 0.03058 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 206.3 Order of pole (three term test) = 192.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4698 1.654 h = 0.0001 0.004 y[1] (numeric) = -0.269216304298 2.75367374164 y[1] (closed_form) = -0.268695914307 2.75436314837 absolute error = 0.0008638 relative error = 0.03121 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 118.1 Order of pole (three term test) = 194.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4699 1.658 h = 0.003 0.006 y[1] (numeric) = -0.28479468885 2.77625348219 y[1] (closed_form) = -0.284310253572 2.77695135488 absolute error = 0.0008495 relative error = 0.03043 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 159.1 Order of pole (three term test) = 197.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4729 1.664 h = 0.0001 0.005 y[1] (numeric) = -0.292463004278 2.82202194707 y[1] (closed_form) = -0.291861016013 2.82283386789 absolute error = 0.001011 relative error = 0.03562 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 72.45 Order of pole (three term test) = 202.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.473 1.669 h = 0.0001 0.003 y[1] (numeric) = -0.312296011783 2.85096269826 y[1] (closed_form) = -0.311757862508 2.85168790393 absolute error = 0.0009031 relative error = 0.03148 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 59.51 Order of pole (three term test) = 206.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4731 1.672 h = 0.001 0.001 y[1] (numeric) = -0.324121060405 2.86861643217 y[1] (closed_form) = -0.323559189516 2.86930640179 absolute error = 0.0008898 relative error = 0.03082 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 47.27 Order of pole (three term test) = 208.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4741 1.673 h = 0.001 0.003 y[1] (numeric) = -0.32249915355 2.87853571608 y[1] (closed_form) = -0.321931568965 2.87920442102 absolute error = 0.0008771 relative error = 0.03027 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 225.3 Order of pole (three term test) = 209.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4751 1.676 h = 0.0001 0.004 y[1] (numeric) = -0.329112439818 2.9000155596 y[1] (closed_form) = -0.328558179612 2.900727235 absolute error = 0.000902 relative error = 0.0309 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 129 Order of pole (three term test) = 212.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4752 1.68 h = 0.003 0.006 y[1] (numeric) = -0.345143126518 2.92378014496 y[1] (closed_form) = -0.344626341763 2.92450106928 absolute error = 0.000887 relative error = 0.03012 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 173.7 Order of pole (three term test) = 215.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4782 1.686 h = 0.0001 0.005 y[1] (numeric) = -0.352654304253 2.97168833187 y[1] (closed_form) = -0.352013407903 2.97252711289 absolute error = 0.001056 relative error = 0.03527 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 79.11 Order of pole (three term test) = 220.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4783 1.691 h = 0.0001 0.003 y[1] (numeric) = -0.373060824343 3.00214631372 y[1] (closed_form) = -0.372487605931 3.00289519759 absolute error = 0.0009431 relative error = 0.03117 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 64.98 memory used=1778.2MB, alloc=52.3MB, time=21.54 Order of pole (three term test) = 225.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4784 1.694 h = 0.001 0.001 y[1] (numeric) = -0.385223426193 3.02072259673 y[1] (closed_form) = -0.384625814544 3.02143439586 absolute error = 0.0009294 relative error = 0.03051 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 51.62 Order of pole (three term test) = 227.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4794 1.695 h = 0.0001 0.004 y[1] (numeric) = -0.383419908662 3.03106961099 y[1] (closed_form) = -0.382816564502 3.03175912602 absolute error = 0.0009162 relative error = 0.02998 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 311.2 Order of pole (three term test) = 228.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4795 1.699 h = 0.003 0.006 y[1] (numeric) = -0.399827720913 3.05584561902 y[1] (closed_form) = -0.399296152989 3.05659461649 absolute error = 0.0009185 relative error = 0.0298 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 187.4 Order of pole (three term test) = 232.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4825 1.705 h = 0.0001 0.005 y[1] (numeric) = -0.407205929716 3.10567342522 y[1] (closed_form) = -0.406544383016 3.10654372067 absolute error = 0.001093 relative error = 0.03489 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 85.36 Order of pole (three term test) = 237.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4826 1.71 h = 0.0001 0.003 y[1] (numeric) = -0.428132461601 3.13749001947 y[1] (closed_form) = -0.427542023361 3.13826754904 absolute error = 0.0009763 relative error = 0.03082 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 70.11 Order of pole (three term test) = 242.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4827 1.713 h = 0.001 0.001 y[1] (numeric) = -0.440601238838 3.15689244456 y[1] (closed_form) = -0.439985797818 3.15763123402 absolute error = 0.0009615 relative error = 0.03016 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 55.7 Order of pole (three term test) = 245.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4837 1.714 h = 0.001 0.003 y[1] (numeric) = -0.438636435202 3.16762375067 y[1] (closed_form) = -0.438015240822 3.16833934185 absolute error = 0.0009476 relative error = 0.02963 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 265.4 Order of pole (three term test) = 246.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4847 1.717 h = 0.0001 0.004 y[1] (numeric) = -0.445370239687 3.19107087824 y[1] (closed_form) = -0.444762601547 3.19183338466 absolute error = 0.000975 relative error = 0.03025 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 152 Order of pole (three term test) = 249.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4848 1.721 h = 0.003 0.006 y[1] (numeric) = -0.462276912923 3.21719182837 y[1] (closed_form) = -0.461709751365 3.21796516103 absolute error = 0.000959 relative error = 0.0295 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 204.6 Order of pole (three term test) = 253.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4878 1.727 h = 0.0001 0.005 y[1] (numeric) = -0.469439543861 3.26933851214 y[1] (closed_form) = -0.468735207318 3.27023714066 absolute error = 0.001142 relative error = 0.03456 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 93.21 Order of pole (three term test) = 259.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4879 1.732 h = 0.0001 0.003 y[1] (numeric) = -0.490956568176 3.30281379122 y[1] (closed_form) = -0.490327571913 3.30361627987 absolute error = 0.00102 relative error = 0.03053 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 76.56 Order of pole (three term test) = 264.3 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1823.2MB, alloc=52.3MB, time=22.08 x[1] = 0.488 1.735 h = 0.001 0.001 y[1] (numeric) = -0.503772273418 3.32322453876 y[1] (closed_form) = -0.503117583661 3.32398626718 absolute error = 0.001004 relative error = 0.02988 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 60.82 Order of pole (three term test) = 267.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.489 1.736 h = 0.001 0.003 y[1] (numeric) = -0.501601373363 3.33441622949 y[1] (closed_form) = -0.500940930869 3.33515365293 absolute error = 0.0009899 relative error = 0.02935 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 289.8 Order of pole (three term test) = 268.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.49 1.739 h = 0.0001 0.004 y[1] (numeric) = -0.508380098561 3.35899035006 y[1] (closed_form) = -0.507733297393 3.35977694834 absolute error = 0.001018 relative error = 0.02997 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 166 Order of pole (three term test) = 271.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4901 1.743 h = 0.003 0.006 y[1] (numeric) = -0.525759161034 3.38647012091 y[1] (closed_form) = -0.525154534381 3.38726848402 absolute error = 0.001001 relative error = 0.02922 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 223.5 Order of pole (three term test) = 275.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4931 1.749 h = 0.0001 0.005 y[1] (numeric) = -0.532670620421 3.44103747303 y[1] (closed_form) = -0.531921255474 3.44196523041 absolute error = 0.001193 relative error = 0.03424 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 101.8 Order of pole (three term test) = 282.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4932 1.754 h = 0.0001 0.003 y[1] (numeric) = -0.554786145642 3.47625256784 y[1] (closed_form) = -0.554116579912 3.4770807063 absolute error = 0.001065 relative error = 0.03025 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 83.6 Order of pole (three term test) = 288.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4933 1.757 h = 0.001 0.001 y[1] (numeric) = -0.567953107812 3.49772082197 y[1] (closed_form) = -0.567257149047 3.49850608177 absolute error = 0.001049 relative error = 0.02961 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 66.42 Order of pole (three term test) = 291.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4943 1.758 h = 0.001 0.003 y[1] (numeric) = -0.565561709172 3.50939128361 y[1] (closed_form) = -0.564860010477 3.51015108204 absolute error = 0.001034 relative error = 0.02909 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 316.5 Order of pole (three term test) = 292.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4953 1.761 h = 0.0001 0.004 y[1] (numeric) = -0.572374788718 3.53514354166 y[1] (closed_form) = -0.571686795431 3.53595487695 absolute error = 0.001064 relative error = 0.0297 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 181.2 Order of pole (three term test) = 296.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4954 1.765 h = 0.003 0.006 y[1] (numeric) = -0.590232296215 3.5640484682 y[1] (closed_form) = -0.589588241317 3.5648725677 absolute error = 0.001046 relative error = 0.02895 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 244 Order of pole (three term test) = 300.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4984 1.771 h = 0.0001 0.005 y[1] (numeric) = -0.596854273581 3.62114245999 y[1] (closed_form) = -0.596057532367 3.62210015313 absolute error = 0.001246 relative error = 0.03394 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 111.1 Order of pole (three term test) = 308.1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1868.0MB, alloc=52.3MB, time=22.63 x[1] = 0.4985 1.776 h = 0.0001 0.003 y[1] (numeric) = -0.619575776366 3.65818223303 y[1] (closed_form) = -0.618863531797 3.65903672097 absolute error = 0.001112 relative error = 0.02998 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 91.29 Order of pole (three term test) = 314.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4986 1.779 h = 0.001 0.001 y[1] (numeric) = -0.633097978282 3.6807594344 y[1] (closed_form) = -0.632358633011 3.6815688224 absolute error = 0.001096 relative error = 0.02935 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 72.53 Order of pole (three term test) = 317.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4996 1.78 h = 0.001 0.003 y[1] (numeric) = -0.630470830001 3.69292772068 y[1] (closed_form) = -0.629725770898 3.69371043912 absolute error = 0.001081 relative error = 0.02884 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 345.6 Order of pole (three term test) = 319.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5006 1.783 h = 0.0001 0.004 y[1] (numeric) = -0.637306660886 3.7199114415 y[1] (closed_form) = -0.636575348179 3.72074816562 absolute error = 0.001111 relative error = 0.02944 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 197.9 Order of pole (three term test) = 322.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5007 1.787 h = 0.003 0.006 y[1] (numeric) = -0.655648212015 3.75031090436 y[1] (closed_form) = -0.6549626698 3.75116145635 absolute error = 0.001092 relative error = 0.02869 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 266.5 Order of pole (three term test) = 327.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5037 1.793 h = 0.0001 0.005 y[1] (numeric) = -0.661939511354 3.81004184526 y[1] (closed_form) = -0.661092931668 3.81103029144 absolute error = 0.001301 relative error = 0.03365 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 121.4 Order of pole (three term test) = 335.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5038 1.798 h = 0.0001 0.003 y[1] (numeric) = -0.685273870991 3.84899505237 y[1] (closed_form) = -0.684516735788 3.84987659768 absolute error = 0.001162 relative error = 0.02972 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 99.69 Order of pole (three term test) = 342.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5039 1.801 h = 0.001 0.001 y[1] (numeric) = -0.699154908634 3.87273499563 y[1] (closed_form) = -0.698369957716 3.87356911219 absolute error = 0.001145 relative error = 0.0291 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 79.2 Order of pole (three term test) = 346.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5049 1.802 h = 0.0001 0.004 y[1] (numeric) = -0.696275865174 3.88542084826 y[1] (closed_form) = -0.695485240984 3.88622703311 absolute error = 0.001129 relative error = 0.0286 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 477.5 Order of pole (three term test) = 347.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.505 1.806 h = 0.003 0.006 y[1] (numeric) = -0.715019557033 3.91709551484 y[1] (closed_form) = -0.714313939402 3.91797985127 absolute error = 0.001131 relative error = 0.02841 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 287.5 Order of pole (three term test) = 353.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.508 1.812 h = 0.0001 0.005 y[1] (numeric) = -0.721024180351 3.97919268266 y[1] (closed_form) = -0.720150052238 3.98021880249 absolute error = 0.001348 relative error = 0.03333 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 131 Order of pole (three term test) = 361.9 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1912.9MB, alloc=52.3MB, time=23.17 x[1] = 0.5081 1.817 h = 0.0001 0.003 y[1] (numeric) = -0.744915375104 4.01985968058 y[1] (closed_form) = -0.744135114599 4.02077556598 absolute error = 0.001203 relative error = 0.02942 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 107.6 Order of pole (three term test) = 369 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5082 1.82 h = 0.001 0.001 y[1] (numeric) = -0.759122607133 4.04464109799 y[1] (closed_form) = -0.758313880656 4.04550746884 absolute error = 0.001185 relative error = 0.02879 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 85.45 Order of pole (three term test) = 373.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5092 1.821 h = 0.001 0.003 y[1] (numeric) = -0.756019592087 4.05779208375 y[1] (closed_form) = -0.755205223836 4.05862939076 absolute error = 0.001168 relative error = 0.02829 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 407.2 Order of pole (three term test) = 374.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5102 1.824 h = 0.0001 0.004 y[1] (numeric) = -0.762879303889 4.0872171367 y[1] (closed_form) = -0.762078721729 4.08811334343 absolute error = 0.001202 relative error = 0.0289 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 233.2 Order of pole (three term test) = 379.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5103 1.828 h = 0.003 0.006 y[1] (numeric) = -0.782154557881 4.12058732789 y[1] (closed_form) = -0.78140335966 4.12149950159 absolute error = 0.001182 relative error = 0.02817 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 314 Order of pole (three term test) = 385.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5133 1.834 h = 0.0001 0.005 y[1] (numeric) = -0.787744993683 4.18553939267 y[1] (closed_form) = -0.78681613302 4.18659784393 absolute error = 0.001408 relative error = 0.03306 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 143 Order of pole (three term test) = 394.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5134 1.839 h = 0.0001 0.003 y[1] (numeric) = -0.812261186505 4.22829586057 y[1] (closed_form) = -0.811431639519 4.22924016924 absolute error = 0.001257 relative error = 0.02919 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 117.5 Order of pole (three term test) = 402.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5135 1.842 h = 0.001 0.001 y[1] (numeric) = -0.826833476061 4.25434670516 y[1] (closed_form) = -0.825974735381 4.25523895717 absolute error = 0.001238 relative error = 0.02857 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 93.31 Order of pole (three term test) = 407.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5145 1.843 h = 0.001 0.003 y[1] (numeric) = -0.823446231853 4.26805411487 y[1] (closed_form) = -0.822581919557 4.26891593415 absolute error = 0.001221 relative error = 0.02808 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 444.6 Order of pole (three term test) = 408.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5155 1.846 h = 0.0001 0.004 y[1] (numeric) = -0.830289855143 4.29887619728 y[1] (closed_form) = -0.829439292501 4.29979971664 absolute error = 0.001256 relative error = 0.02867 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 254.6 Order of pole (three term test) = 413.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5156 1.85 h = 0.003 0.006 y[1] (numeric) = -0.850063100311 4.33395738368 y[1] (closed_form) = -0.849263963008 4.33489813746 absolute error = 0.001234 relative error = 0.02794 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 342.8 Order of pole (three term test) = 420.1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1957.8MB, alloc=52.3MB, time=23.71 x[1] = 0.5186 1.856 h = 0.0001 0.005 y[1] (numeric) = -0.855188938981 4.40188802425 y[1] (closed_form) = -0.854202526758 4.40297965076 absolute error = 0.001471 relative error = 0.0328 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 156.2 Order of pole (three term test) = 430.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5187 1.861 h = 0.0001 0.003 y[1] (numeric) = -0.880334948244 4.44683481894 y[1] (closed_form) = -0.879453583402 4.44780827918 absolute error = 0.001313 relative error = 0.02896 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 128.3 Order of pole (three term test) = 438.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5188 1.864 h = 0.001 0.001 y[1] (numeric) = -0.895274565304 4.47421620057 y[1] (closed_form) = -0.894363274375 4.47513493984 absolute error = 0.001294 relative error = 0.02836 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 101.9 Order of pole (three term test) = 443.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5198 1.865 h = 0.001 0.003 y[1] (numeric) = -0.891584123967 4.48850187384 y[1] (closed_form) = -0.890667349817 4.4893887508 absolute error = 0.001276 relative error = 0.02787 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 485.5 Order of pole (three term test) = 445.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5208 1.868 h = 0.0001 0.004 y[1] (numeric) = -0.898395380873 4.52078358606 y[1] (closed_form) = -0.897492287445 4.52173508882 absolute error = 0.001312 relative error = 0.02846 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 278.1 Order of pole (three term test) = 451 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5209 1.872 h = 0.003 0.006 y[1] (numeric) = -0.918669946868 4.55765820039 y[1] (closed_form) = -0.91782039789 4.55862828444 absolute error = 0.001289 relative error = 0.02773 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 374.4 Order of pole (three term test) = 458.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5239 1.878 h = 0.0001 0.005 y[1] (numeric) = -0.923277152176 4.62869609452 y[1] (closed_form) = -0.922230233463 4.6298217469 absolute error = 0.001537 relative error = 0.03256 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 170.5 Order of pole (three term test) = 469.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.524 1.883 h = 0.0001 0.003 y[1] (numeric) = -0.949056901179 4.67593865531 y[1] (closed_form) = -0.9481210654 4.67694200023 absolute error = 0.001372 relative error = 0.02875 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 140.1 Order of pole (three term test) = 478.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5241 1.886 h = 0.001 0.001 y[1] (numeric) = -0.964365544167 4.70471445326 y[1] (closed_form) = -0.963399046387 4.70566028521 absolute error = 0.001352 relative error = 0.02815 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 111.3 Order of pole (three term test) = 484 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5251 1.887 h = 0.001 0.003 y[1] (numeric) = -0.960351845185 4.71960100145 y[1] (closed_form) = -0.959379972306 4.72051347826 absolute error = 0.001333 relative error = 0.02767 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 530.2 Order of pole (three term test) = 486 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5261 1.89 h = 0.0001 0.004 y[1] (numeric) = -0.967113036847 4.75340757579 y[1] (closed_form) = -0.96615474041 4.75438773475 absolute error = 0.001371 relative error = 0.02825 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 303.6 Order of pole (three term test) = 491.8 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2002.7MB, alloc=52.3MB, time=24.26 x[1] = 0.5262 1.894 h = 0.003 0.006 y[1] (numeric) = -0.987891494231 4.79216178948 y[1] (closed_form) = -0.986988941673 4.79316196045 absolute error = 0.001347 relative error = 0.02753 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 408.8 Order of pole (three term test) = 499.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5292 1.9 h = 0.0001 0.005 y[1] (numeric) = -0.991922184714 4.86644079815 y[1] (closed_form) = -0.990811662476 4.86760133262 absolute error = 0.001606 relative error = 0.03234 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 186.2 Order of pole (three term test) = 511.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5293 1.905 h = 0.0001 0.003 y[1] (numeric) = -1.01833861046 4.91608934279 y[1] (closed_form) = -1.01734552343 4.91712330919 absolute error = 0.001434 relative error = 0.02855 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 152.9 Order of pole (three term test) = 521.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5294 1.908 h = 0.001 0.001 y[1] (numeric) = -1.03401734974 4.94632632389 y[1] (closed_form) = -1.03299286253 4.9472998518 absolute error = 0.001413 relative error = 0.02796 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 121.5 Order of pole (three term test) = 527.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5304 1.909 h = 0.0001 0.004 y[1] (numeric) = -1.02965918235 4.96183715264 y[1] (closed_form) = -1.02862944949 4.96277576674 absolute error = 0.001393 relative error = 0.02749 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 732.6 Order of pole (three term test) = 530 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5305 1.913 h = 0.003 0.006 y[1] (numeric) = -1.05085417676 5.00219442248 y[1] (closed_form) = -1.04992464429 5.00323511104 absolute error = 0.001395 relative error = 0.02729 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 441.1 Order of pole (three term test) = 538.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5335 1.919 h = 0.0001 0.005 y[1] (numeric) = -1.05438004538 5.07938244623 y[1] (closed_form) = -1.05323305522 5.08058783958 absolute error = 0.001664 relative error = 0.03207 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 200.9 Order of pole (three term test) = 551.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5336 1.924 h = 0.0001 0.003 y[1] (numeric) = -1.08137656809 5.13118642806 y[1] (closed_form) = -1.08035269372 5.13226140783 absolute error = 0.001485 relative error = 0.02831 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 165 Order of pole (three term test) = 562.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5337 1.927 h = 0.001 0.001 y[1] (numeric) = -1.09739275122 5.16273249405 y[1] (closed_form) = -1.09633680341 5.16374441444 absolute error = 0.001463 relative error = 0.02771 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 131.1 Order of pole (three term test) = 568.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5347 1.928 h = 0.001 0.003 y[1] (numeric) = -1.09272800021 5.17880451837 y[1] (closed_form) = -1.09166691684 5.17978012657 absolute error = 0.001441 relative error = 0.02723 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 624.7 Order of pole (three term test) = 571.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5357 1.931 h = 0.0001 0.004 y[1] (numeric) = -1.09936379599 5.21563273407 y[1] (closed_form) = -1.09831603071 5.21668208057 absolute error = 0.001483 relative error = 0.02782 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 357.8 Order of pole (three term test) = 578 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2047.6MB, alloc=52.3MB, time=24.80 x[1] = 0.5358 1.935 h = 0.003 0.006 y[1] (numeric) = -1.1211087992 5.25812123226 y[1] (closed_form) = -1.12012111304 5.25919346372 absolute error = 0.001458 relative error = 0.02711 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 481.7 Order of pole (three term test) = 587.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5388 1.941 h = 0.0001 0.005 y[1] (numeric) = -1.12394116565 5.33881471424 y[1] (closed_form) = -1.1227244189 5.34005663436 absolute error = 0.001739 relative error = 0.03186 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 219.4 Order of pole (three term test) = 601.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5389 1.946 h = 0.0001 0.003 y[1] (numeric) = -1.1515783233 5.39324318875 y[1] (closed_form) = -1.15049167446 5.39435020341 absolute error = 0.001551 relative error = 0.02812 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 180.2 Order of pole (three term test) = 613.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.539 1.949 h = 0.001 0.001 y[1] (numeric) = -1.16796559549 5.42638279254 y[1] (closed_form) = -1.16684613284 5.42742355764 absolute error = 0.001529 relative error = 0.02753 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 143.2 Order of pole (three term test) = 620.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.54 1.95 h = 0.001 0.003 y[1] (numeric) = -1.16291393914 5.44312513042 y[1] (closed_form) = -1.16178951376 5.4441278945 absolute error = 0.001507 relative error = 0.02706 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 682.2 Order of pole (three term test) = 622.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.541 1.953 h = 0.0001 0.004 y[1] (numeric) = -1.16944122605 5.48168056485 y[1] (closed_form) = -1.16832989766 5.48276052881 absolute error = 0.00155 relative error = 0.02764 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 390.7 Order of pole (three term test) = 630.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5411 1.957 h = 0.003 0.006 y[1] (numeric) = -1.19169377379 5.5263172859 y[1] (closed_form) = -1.19064496993 5.52742183093 absolute error = 0.001523 relative error = 0.02694 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 526 Order of pole (three term test) = 640.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5441 1.963 h = 0.0001 0.005 y[1] (numeric) = -1.19376251009 5.61066604133 y[1] (closed_form) = -1.19247246664 5.61194535464 absolute error = 0.001817 relative error = 0.03167 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 239.6 Order of pole (three term test) = 655.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5442 1.968 h = 0.0001 0.003 y[1] (numeric) = -1.22203992226 5.66784406538 y[1] (closed_form) = -1.22088732199 5.66898385669 absolute error = 0.001621 relative error = 0.02795 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 196.8 Order of pole (three term test) = 668.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5443 1.971 h = 0.001 0.001 y[1] (numeric) = -1.23879724933 5.70265293915 y[1] (closed_form) = -1.23761109686 5.70372313927 absolute error = 0.001598 relative error = 0.02737 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 156.3 Order of pole (three term test) = 676.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5453 1.972 h = 0.001 0.003 y[1] (numeric) = -1.2333338522 5.72009141241 y[1] (closed_form) = -1.23214293624 5.72112184874 absolute error = 0.001575 relative error = 0.02691 % Correct digits = 4 memory used=2092.4MB, alloc=52.3MB, time=25.34 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 744.9 Order of pole (three term test) = 679.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5463 1.975 h = 0.0001 0.004 y[1] (numeric) = -1.23972855956 5.76045047517 y[1] (closed_form) = -1.23855047133 5.761561726 absolute error = 0.001619 relative error = 0.02748 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 426.6 Order of pole (three term test) = 687.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5464 1.979 h = 0.003 0.006 y[1] (numeric) = -1.26248758721 5.80733759303 y[1] (closed_form) = -1.26137456003 5.80847522419 absolute error = 0.001592 relative error = 0.02678 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 574.4 Order of pole (three term test) = 698.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5494 1.985 h = 0.0001 0.005 y[1] (numeric) = -1.26371776199 5.89549739123 y[1] (closed_form) = -1.26235071317 5.89681496395 absolute error = 0.001899 relative error = 0.03148 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 261.6 Order of pole (three term test) = 715.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5495 1.99 h = 0.0001 0.003 y[1] (numeric) = -1.29263365041 5.95555563383 y[1] (closed_form) = -1.29141177089 5.95672894181 absolute error = 0.001694 relative error = 0.02779 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 214.9 Order of pole (three term test) = 729.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5496 1.993 h = 0.001 0.001 y[1] (numeric) = -1.30975911553 5.99211289955 y[1] (closed_form) = -1.30850294917 5.99321311647 absolute error = 0.00167 relative error = 0.02722 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 170.7 Order of pole (three term test) = 738.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5506 1.994 h = 0.001 0.003 y[1] (numeric) = -1.30385774169 6.01027421544 y[1] (closed_form) = -1.30259703949 6.01133282883 absolute error = 0.001646 relative error = 0.02676 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 813.4 Order of pole (three term test) = 741.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5516 1.997 h = 0.0001 0.004 y[1] (numeric) = -1.31009387407 6.052516482 y[1] (closed_form) = -1.30884567834 6.05365968387 absolute error = 0.001693 relative error = 0.02733 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 465.9 Order of pole (three term test) = 749.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5517 2.001 h = 0.003 0.006 y[1] (numeric) = -1.33335714098 6.10176074756 y[1] (closed_form) = -1.33217663685 6.10293223785 absolute error = 0.001663 relative error = 0.02662 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 627.2 Order of pole (three term test) = 761.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5547 2.007 h = 0.0001 0.005 y[1] (numeric) = -1.33366873742 6.19389352616 y[1] (closed_form) = -1.3322207984 6.19525022244 absolute error = 0.001984 relative error = 0.03131 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 285.7 Order of pole (three term test) = 780.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5548 2.012 h = 0.0001 0.003 y[1] (numeric) = -1.36321980082 6.25696850517 y[1] (closed_form) = -1.36192515661 6.25817606629 absolute error = 0.00177 relative error = 0.02764 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 234.6 Order of pole (three term test) = 795.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5549 2.015 h = 0.001 0.001 y[1] (numeric) = -1.3807105272 6.2953568171 y[1] (closed_form) = -1.37938086716 6.296487622 absolute error = 0.001745 relative error = 0.02708 % Correct digits = 4 memory used=2137.2MB, alloc=52.3MB, time=25.89 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 186.4 Order of pole (three term test) = 805.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5559 2.016 h = 0.0001 0.004 y[1] (numeric) = -1.37434346743 6.31426859256 y[1] (closed_form) = -1.37300952975 6.31535587408 absolute error = 0.001721 relative error = 0.02663 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1124 Order of pole (three term test) = 808.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.556 2.02 h = 0.003 0.006 y[1] (numeric) = -1.3980204643 6.36552235416 y[1] (closed_form) = -1.39680401645 6.36674225687 absolute error = 0.001723 relative error = 0.02643 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 676.7 Order of pole (three term test) = 821.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.559 2.026 h = 0.0001 0.005 y[1] (numeric) = -1.39752327277 6.46122182912 y[1] (closed_form) = -1.39602738064 6.46263171063 absolute error = 0.002056 relative error = 0.03109 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 308.2 Order of pole (three term test) = 841 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5591 2.031 h = 0.0001 0.003 y[1] (numeric) = -1.42765543119 6.52699999919 y[1] (closed_form) = -1.4263201025 6.52825634639 absolute error = 0.001833 relative error = 0.02744 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 253.2 Order of pole (three term test) = 857.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5592 2.034 h = 0.001 0.001 y[1] (numeric) = -1.44548068504 6.56702912314 y[1] (closed_form) = -1.44410967268 6.56820542985 absolute error = 0.001806 relative error = 0.02686 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 201.1 Order of pole (three term test) = 867.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5602 2.035 h = 0.001 0.003 y[1] (numeric) = -1.43869881307 6.5866157221 y[1] (closed_form) = -1.43732374728 6.58774678263 absolute error = 0.00178 relative error = 0.02641 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 958.4 Order of pole (three term test) = 871.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5612 2.038 h = 0.0001 0.004 y[1] (numeric) = -1.44458840962 6.63258805217 y[1] (closed_form) = -1.44322514957 6.63381117604 absolute error = 0.001832 relative error = 0.02698 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 548.9 Order of pole (three term test) = 881.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5613 2.042 h = 0.003 0.006 y[1] (numeric) = -1.46881082728 6.68651314329 y[1] (closed_form) = -1.46752044046 6.68776838215 absolute error = 0.0018 relative error = 0.02629 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 739 Order of pole (three term test) = 895.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5643 2.048 h = 0.0001 0.005 y[1] (numeric) = -1.46723371366 6.7865052151 y[1] (closed_form) = -1.46564921663 6.78795586709 absolute error = 0.002148 relative error = 0.03094 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 336.6 Order of pole (three term test) = 917.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5644 2.053 h = 0.0001 0.003 y[1] (numeric) = -1.49799218968 6.85557065415 y[1] (closed_form) = -1.49657717539 6.85686265521 absolute error = 0.001916 relative error = 0.0273 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 276.5 Order of pole (three term test) = 935.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5645 2.056 h = 0.001 0.001 y[1] (numeric) = -1.51617560165 6.89759460255 y[1] (closed_form) = -1.51472418877 6.8988025704 absolute error = 0.001888 relative error = 0.02673 % Correct digits = 4 memory used=2182.2MB, alloc=52.3MB, time=26.43 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 219.6 Order of pole (three term test) = 946.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5655 2.057 h = 0.001 0.003 y[1] (numeric) = -1.50887265382 6.91798593022 y[1] (closed_form) = -1.50741750763 6.91914657378 absolute error = 0.001861 relative error = 0.02628 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1047 Order of pole (three term test) = 950.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5665 2.06 h = 0.0001 0.004 y[1] (numeric) = -1.51451864784 6.96608808993 y[1] (closed_form) = -1.51307481594 6.96734506472 absolute error = 0.001914 relative error = 0.02685 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 599.4 Order of pole (three term test) = 962 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5666 2.064 h = 0.003 0.006 y[1] (numeric) = -1.53923291589 7.02270283151 y[1] (closed_form) = -1.53786487527 7.02399417326 absolute error = 0.001881 relative error = 0.02616 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 807 Order of pole (three term test) = 977.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5696 2.07 h = 0.0001 0.005 y[1] (numeric) = -1.53647970281 7.1271683986 y[1] (closed_form) = -1.5348021673 7.12866066978 absolute error = 0.002245 relative error = 0.03079 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 367.6 Order of pole (three term test) = 1001 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5697 2.075 h = 0.0001 0.003 y[1] (numeric) = -1.56785615129 7.19967577149 y[1] (closed_form) = -1.56635747497 7.2010041439 absolute error = 0.002003 relative error = 0.02718 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 301.9 Order of pole (three term test) = 1021 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5698 2.078 h = 0.001 0.001 y[1] (numeric) = -1.58639167323 7.24378815611 y[1] (closed_form) = -1.58485589543 7.24502831539 absolute error = 0.001974 relative error = 0.02662 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 239.8 Order of pole (three term test) = 1033 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5708 2.079 h = 0.001 0.003 y[1] (numeric) = -1.57853530328 7.26501458886 y[1] (closed_form) = -1.57699614964 7.26620525593 absolute error = 0.001946 relative error = 0.02617 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1143 Order of pole (three term test) = 1037 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5718 2.082 h = 0.0001 0.004 y[1] (numeric) = -1.58390310886 7.31533957726 y[1] (closed_form) = -1.5823747088 7.3166310297 absolute error = 0.002001 relative error = 0.02673 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 654.5 Order of pole (three term test) = 1049 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5719 2.086 h = 0.003 0.006 y[1] (numeric) = -1.609101476 7.37477028626 y[1] (closed_form) = -1.60765189144 7.37609849103 absolute error = 0.001966 relative error = 0.02604 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 881.2 Order of pole (three term test) = 1066 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5749 2.092 h = 0.0001 0.005 y[1] (numeric) = -1.60506966693 7.48389730861 y[1] (closed_form) = -1.60329445085 7.4854320368 absolute error = 0.002347 relative error = 0.03065 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 401.4 Order of pole (three term test) = 1092 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.575 2.097 h = 0.0001 0.003 y[1] (numeric) = -1.63705365819 7.56000813438 y[1] (closed_form) = -1.63546715691 7.56137358392 absolute error = 0.002093 relative error = 0.02706 % Correct digits = 4 memory used=2227.1MB, alloc=52.3MB, time=26.98 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 329.7 Order of pole (three term test) = 1114 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5751 2.1 h = 0.001 0.001 y[1] (numeric) = -1.65593393549 7.60630670456 y[1] (closed_form) = -1.65430964446 7.60757956552 absolute error = 0.002064 relative error = 0.02651 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 261.9 Order of pole (three term test) = 1127 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5761 2.101 h = 0.001 0.003 y[1] (numeric) = -1.6474900086 7.62839962545 y[1] (closed_form) = -1.64586273921 7.62962073287 absolute error = 0.002034 relative error = 0.02607 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1248 Order of pole (three term test) = 1131 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5771 2.104 h = 0.0001 0.004 y[1] (numeric) = -1.65254245835 7.68104423611 y[1] (closed_form) = -1.65092530742 7.68237077689 absolute error = 0.002092 relative error = 0.02662 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 714.7 Order of pole (three term test) = 1145 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5772 2.108 h = 0.003 0.006 y[1] (numeric) = -1.67821542867 7.74342281709 y[1] (closed_form) = -1.67668022692 7.74478863615 absolute error = 0.002055 relative error = 0.02593 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 962.3 Order of pole (three term test) = 1163 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5802 2.114 h = 0.0001 0.005 y[1] (numeric) = -1.67279584559 7.85740656343 y[1] (closed_form) = -1.67091808906 7.85898457271 absolute error = 0.002453 relative error = 0.03053 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 438.3 Order of pole (three term test) = 1191 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5803 2.119 h = 0.0001 0.003 y[1] (numeric) = -1.70537469571 7.93728950013 y[1] (closed_form) = -1.70369601172 7.93869271824 absolute error = 0.002188 relative error = 0.02695 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 360 Order of pole (three term test) = 1215 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5804 2.122 h = 0.001 0.001 y[1] (numeric) = -1.72459096262 7.98587631414 y[1] (closed_form) = -1.72287381809 7.9871823641 absolute error = 0.002157 relative error = 0.0264 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 286 Order of pole (three term test) = 1229 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5814 2.123 h = 0.0001 0.004 y[1] (numeric) = -1.71552346383 8.00886813833 y[1] (closed_form) = -1.7138037813 8.01012007626 absolute error = 0.002127 relative error = 0.02597 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1724 Order of pole (three term test) = 1234 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5815 2.127 h = 0.003 0.006 y[1] (numeric) = -1.74158109636 8.07375878422 y[1] (closed_form) = -1.73999836594 8.07518221709 absolute error = 0.002129 relative error = 0.02577 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1038 Order of pole (three term test) = 1254 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5845 2.133 h = 0.0001 0.005 y[1] (numeric) = -1.73493531448 8.19210360322 y[1] (closed_form) = -1.73299487345 8.1937443733 absolute error = 0.002541 relative error = 0.03034 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 472.9 Order of pole (three term test) = 1284 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5846 2.138 h = 0.0001 0.003 y[1] (numeric) = -1.7680619945 8.27536733793 y[1] (closed_form) = -1.7663298942 8.27682833334 absolute error = 0.002266 relative error = 0.02677 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 388.4 Order of pole (three term test) = 1310 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2272.2MB, alloc=52.3MB, time=27.52 x[1] = 0.5847 2.141 h = 0.001 0.001 y[1] (numeric) = -1.78758828716 8.32600511078 y[1] (closed_form) = -1.78581710722 8.32736483344 absolute error = 0.002233 relative error = 0.02622 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 308.6 Order of pole (three term test) = 1326 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5857 2.142 h = 0.001 0.003 y[1] (numeric) = -1.77796494544 8.34980549371 y[1] (closed_form) = -1.7761916134 8.35110898746 absolute error = 0.002201 relative error = 0.02578 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1470 Order of pole (three term test) = 1331 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5867 2.145 h = 0.0001 0.004 y[1] (numeric) = -1.78235270352 8.40704252343 y[1] (closed_form) = -1.78058815213 8.40846065245 absolute error = 0.002264 relative error = 0.02634 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 842.1 Order of pole (three term test) = 1347 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5868 2.149 h = 0.003 0.006 y[1] (numeric) = -1.80891606105 8.47527228886 y[1] (closed_form) = -1.80723962715 8.47673475598 absolute error = 0.002225 relative error = 0.02567 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1134 Order of pole (three term test) = 1368 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5898 2.155 h = 0.0001 0.005 y[1] (numeric) = -1.80066279015 8.59885901669 y[1] (closed_form) = -1.798610162 8.60054461874 absolute error = 0.002656 relative error = 0.03023 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 516.4 Order of pole (three term test) = 1401 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5899 2.16 h = 0.0001 0.003 y[1] (numeric) = -1.83435632466 8.68622894091 y[1] (closed_form) = -1.83252339254 8.68772900142 absolute error = 0.002369 relative error = 0.02668 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 424.2 Order of pole (three term test) = 1429 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.59 2.163 h = 0.001 0.001 y[1] (numeric) = -1.85419949949 8.73935709661 y[1] (closed_form) = -1.85232685506 8.74075090048 absolute error = 0.002334 relative error = 0.02613 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 337 Order of pole (three term test) = 1446 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.591 2.164 h = 0.001 0.003 y[1] (numeric) = -1.84388065084 8.7641200208 y[1] (closed_form) = -1.84200638126 8.76545504538 absolute error = 0.002301 relative error = 0.02569 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1606 Order of pole (three term test) = 1452 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.592 2.167 h = 0.0001 0.004 y[1] (numeric) = -1.84783233684 8.82397638006 y[1] (closed_form) = -1.845965971 8.82543128815 absolute error = 0.002366 relative error = 0.02625 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 919.5 Order of pole (three term test) = 1470 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5921 2.171 h = 0.003 0.006 y[1] (numeric) = -1.87483401988 8.89556452807 y[1] (closed_form) = -1.87305923909 8.89706674379 absolute error = 0.002325 relative error = 0.02557 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1238 Order of pole (three term test) = 1493 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5951 2.177 h = 0.0001 0.005 y[1] (numeric) = -1.86484289054 9.02461086673 y[1] (closed_form) = -1.86267253754 9.02634207106 absolute error = 0.002776 relative error = 0.03012 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 563.9 Order of pole (three term test) = 1529 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2317.1MB, alloc=52.3MB, time=28.07 x[1] = 0.5952 2.182 h = 0.0001 0.003 y[1] (numeric) = -1.89908320786 9.11627776852 y[1] (closed_form) = -1.89714448002 9.11781753101 absolute error = 0.002476 relative error = 0.02658 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 463.2 Order of pole (three term test) = 1560 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5953 2.185 h = 0.001 0.001 y[1] (numeric) = -1.91922988274 9.17201171991 y[1] (closed_form) = -1.91725083662 9.17344001103 absolute error = 0.002441 relative error = 0.02604 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 368 Order of pole (three term test) = 1578 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5963 2.186 h = 0.001 0.003 y[1] (numeric) = -1.90817360129 9.19777272073 y[1] (closed_form) = -1.90619350888 9.19913957347 absolute error = 0.002406 relative error = 0.02561 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1753 Order of pole (three term test) = 1585 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5973 2.189 h = 0.0001 0.004 y[1] (numeric) = -1.91164057149 9.26036126549 y[1] (closed_form) = -1.90966740844 9.26185347598 absolute error = 0.002474 relative error = 0.02616 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1004 Order of pole (three term test) = 1604 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5974 2.193 h = 0.003 0.006 y[1] (numeric) = -1.9390630292 9.33546355657 y[1] (closed_form) = -1.93718504166 9.33700621597 absolute error = 0.00243 relative error = 0.02549 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1352 Order of pole (three term test) = 1629 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6004 2.199 h = 0.0001 0.005 y[1] (numeric) = -1.92719540814 9.47019554396 y[1] (closed_form) = -1.9249015353 9.47197309418 absolute error = 0.002902 relative error = 0.03002 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 615.8 Order of pole (three term test) = 1669 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6005 2.204 h = 0.0001 0.003 y[1] (numeric) = -1.96195942441 9.56635855859 y[1] (closed_form) = -1.95990970693 9.56793863365 absolute error = 0.002588 relative error = 0.0265 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 505.8 Order of pole (three term test) = 1702 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6006 2.207 h = 0.001 0.001 y[1] (numeric) = -1.9823943393 9.62481875426 y[1] (closed_form) = -1.98030372806 9.62628190229 absolute error = 0.002552 relative error = 0.02596 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 401.8 Order of pole (three term test) = 1722 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6016 2.208 h = 0.001 0.003 y[1] (numeric) = -1.97055642296 9.65161449934 y[1] (closed_form) = -1.96846539969 9.65301343687 absolute error = 0.002516 relative error = 0.02554 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1915 Order of pole (three term test) = 1729 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6026 2.211 h = 0.0001 0.004 y[1] (numeric) = -1.97348660022 9.71705261635 y[1] (closed_form) = -1.97140142762 9.71858262099 absolute error = 0.002586 relative error = 0.02608 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1096 Order of pole (three term test) = 1750 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6027 2.215 h = 0.003 0.006 y[1] (numeric) = -2.00130977019 9.79583161286 y[1] (closed_form) = -1.99932349008 9.79741538848 absolute error = 0.00254 relative error = 0.02541 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1476 Order of pole (three term test) = 1778 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2362.1MB, alloc=52.3MB, time=28.61 x[1] = 0.6057 2.221 h = 0.0001 0.005 y[1] (numeric) = -1.98741829651 9.93648390572 y[1] (closed_form) = -1.98499484032 9.93830851472 absolute error = 0.003034 relative error = 0.02993 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 672.4 Order of pole (three term test) = 1821 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6058 2.226 h = 0.0001 0.003 y[1] (numeric) = -2.02267968778 10.0373508573 y[1] (closed_form) = -2.02051354671 10.0389718255 absolute error = 0.002705 relative error = 0.02642 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 552.3 Order of pole (three term test) = 1857 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6059 2.229 h = 0.001 0.001 y[1] (numeric) = -2.04338556454 10.0986629871 y[1] (closed_form) = -2.04117798876 10.1001613211 absolute error = 0.002668 relative error = 0.02589 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 438.8 Order of pole (three term test) = 1880 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6069 2.23 h = 0.0001 0.004 y[1] (numeric) = -2.03071942012 10.1265313019 y[1] (closed_form) = -2.02851212573 10.1279625359 absolute error = 0.002631 relative error = 0.02547 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2645 Order of pole (three term test) = 1887 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.607 2.234 h = 0.003 0.006 y[1] (numeric) = -2.05885961571 10.2084421888 y[1] (closed_form) = -2.05681089682 10.21009423 absolute error = 0.002632 relative error = 0.02527 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1593 Order of pole (three term test) = 1917 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.61 2.24 h = 0.0001 0.005 y[1] (numeric) = -2.04317554454 10.3544118538 y[1] (closed_form) = -2.04067057772 10.3563101392 absolute error = 0.003143 relative error = 0.02978 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 725.5 Order of pole (three term test) = 1964 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6101 2.245 h = 0.0001 0.003 y[1] (numeric) = -2.07890089919 10.4594956798 y[1] (closed_form) = -2.07666502623 10.4611847445 absolute error = 0.002802 relative error = 0.02627 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 595.9 Order of pole (three term test) = 2003 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6102 2.248 h = 0.001 0.001 y[1] (numeric) = -2.09986063618 10.52336456 y[1] (closed_form) = -2.09758282156 10.5249258743 absolute error = 0.002762 relative error = 0.02573 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 473.4 Order of pole (three term test) = 2027 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6112 2.249 h = 0.001 0.003 y[1] (numeric) = -2.08645576756 10.5521979677 y[1] (closed_form) = -2.08417884517 10.5536895877 absolute error = 0.002722 relative error = 0.0253 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2256 Order of pole (three term test) = 2035 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6122 2.252 h = 0.0001 0.004 y[1] (numeric) = -2.08827334253 10.6232751473 y[1] (closed_form) = -2.0860000357 10.6249091325 absolute error = 0.0028 relative error = 0.02586 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1292 Order of pole (three term test) = 2059 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6123 2.256 h = 0.003 0.006 y[1] (numeric) = -2.11682805865 10.7093486823 y[1] (closed_form) = -2.1146609552 10.7110430863 absolute error = 0.002751 relative error = 0.0252 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1739 Order of pole (three term test) = 2092 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2407.0MB, alloc=52.3MB, time=29.16 x[1] = 0.6153 2.262 h = 0.0001 0.005 y[1] (numeric) = -2.09882406411 10.8617012582 y[1] (closed_form) = -2.09617748337 10.8636479123 absolute error = 0.003285 relative error = 0.02969 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 792.2 Order of pole (three term test) = 2143 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6154 2.267 h = 0.0001 0.003 y[1] (numeric) = -2.13499108461 10.9719004993 y[1] (closed_form) = -2.13262800763 10.9736315154 absolute error = 0.002929 relative error = 0.0262 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 650.7 Order of pole (three term test) = 2186 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6155 2.27 h = 0.001 0.001 y[1] (numeric) = -2.15618540008 11.0388701481 y[1] (closed_form) = -2.15377991318 11.040467209 absolute error = 0.002887 relative error = 0.02567 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 517 Order of pole (three term test) = 2212 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6165 2.271 h = 0.001 0.003 y[1] (numeric) = -2.14185930856 11.068850307 y[1] (closed_form) = -2.1394555266 11.0703745521 absolute error = 0.002846 relative error = 0.02524 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2463 Order of pole (three term test) = 2221 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6175 2.274 h = 0.0001 0.004 y[1] (numeric) = -2.14297186809 11.1431401741 y[1] (closed_form) = -2.14057028593 11.144813221 absolute error = 0.002927 relative error = 0.02579 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1411 Order of pole (three term test) = 2248 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6176 2.278 h = 0.003 0.006 y[1] (numeric) = -2.17185653353 11.233395915 y[1] (closed_form) = -2.16956525673 11.2351332727 absolute error = 0.002875 relative error = 0.02513 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1899 Order of pole (three term test) = 2284 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6206 2.284 h = 0.0001 0.005 y[1] (numeric) = -2.15135762145 11.3923924699 y[1] (closed_form) = -2.14856252814 11.3943880962 absolute error = 0.003434 relative error = 0.02962 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 865.1 Order of pole (three term test) = 2339 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6207 2.289 h = 0.0001 0.003 y[1] (numeric) = -2.18792944574 11.5079418592 y[1] (closed_form) = -2.18543298436 11.5097153015 absolute error = 0.003062 relative error = 0.02614 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 710.6 Order of pole (three term test) = 2386 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6208 2.292 h = 0.001 0.001 y[1] (numeric) = -2.20933450654 11.5781541949 y[1] (closed_form) = -2.20679521464 11.5797871933 absolute error = 0.003019 relative error = 0.02561 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 564.5 Order of pole (three term test) = 2414 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6218 2.293 h = 0.001 0.003 y[1] (numeric) = -2.19403308956 11.6093224168 y[1] (closed_form) = -2.19149638634 11.6108793467 absolute error = 0.002976 relative error = 0.02519 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2690 Order of pole (three term test) = 2424 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6228 2.296 h = 0.0001 0.004 y[1] (numeric) = -2.19437334414 11.6869615027 y[1] (closed_form) = -2.19183729014 11.6886739444 absolute error = 0.00306 relative error = 0.02573 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1541 Order of pole (three term test) = 2453 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2452.0MB, alloc=52.3MB, time=29.70 x[1] = 0.6229 2.3 h = 0.003 0.006 y[1] (numeric) = -2.22355642389 11.7815910137 y[1] (closed_form) = -2.2211349184 11.7833718784 absolute error = 0.003006 relative error = 0.02507 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2074 Order of pole (three term test) = 2492 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6259 2.306 h = 0.0001 0.005 y[1] (numeric) = -2.20037685037 11.9475024055 y[1] (closed_form) = -2.19742602928 11.9495475582 absolute error = 0.00359 relative error = 0.02955 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 944.7 Order of pole (three term test) = 2552 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.626 2.311 h = 0.0001 0.003 y[1] (numeric) = -2.23731236255 12.0686468118 y[1] (closed_form) = -2.23467605352 12.0704631079 absolute error = 0.003201 relative error = 0.02608 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 776 Order of pole (three term test) = 2604 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6261 2.314 h = 0.001 0.001 y[1] (numeric) = -2.25890169421 12.1422498635 y[1] (closed_form) = -2.25622218699 12.1439189308 absolute error = 0.003157 relative error = 0.02556 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 616.4 Order of pole (three term test) = 2635 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6271 2.315 h = 0.001 0.003 y[1] (numeric) = -2.24256796182 12.1746487168 y[1] (closed_form) = -2.23989200272 12.1762383266 absolute error = 0.003112 relative error = 0.02514 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2937 Order of pole (three term test) = 2645 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6281 2.318 h = 0.0001 0.004 y[1] (numeric) = -2.24206408826 12.2557789406 y[1] (closed_form) = -2.23938708388 12.2575310566 absolute error = 0.003199 relative error = 0.02568 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1682 Order of pole (three term test) = 2677 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6282 2.322 h = 0.003 0.006 y[1] (numeric) = -2.27151051049 12.3549820415 y[1] (closed_form) = -2.26895244285 12.3568069242 absolute error = 0.003142 relative error = 0.02501 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2265 Order of pole (three term test) = 2720 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6312 2.328 h = 0.0001 0.005 y[1] (numeric) = -2.2454531904 12.5280892383 y[1] (closed_form) = -2.24233909607 12.5301844167 absolute error = 0.003753 relative error = 0.02949 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1032 Order of pole (three term test) = 2786 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6313 2.333 h = 0.0001 0.003 y[1] (numeric) = -2.28270671724 12.655084074 y[1] (closed_form) = -2.27992380229 12.6569435992 absolute error = 0.003347 relative error = 0.02603 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 847.3 Order of pole (three term test) = 2842 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6314 2.336 h = 0.001 0.001 y[1] (numeric) = -2.30445101756 12.7322322269 y[1] (closed_form) = -2.30162459532 12.7339374297 absolute error = 0.003301 relative error = 0.02551 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 673.1 Order of pole (three term test) = 2876 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6324 2.337 h = 0.0001 0.004 y[1] (numeric) = -2.28702494872 12.7659055613 y[1] (closed_form) = -2.28420311467 12.767527776 absolute error = 0.003255 relative error = 0.0251 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4059 Order of pole (three term test) = 2887 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2497.0MB, alloc=52.3MB, time=30.24 x[1] = 0.6325 2.341 h = 0.003 0.006 y[1] (numeric) = -2.31666563457 12.8690029927 y[1] (closed_form) = -2.31402601292 12.8709083766 absolute error = 0.003255 relative error = 0.02489 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2444 Order of pole (three term test) = 2934 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6355 2.347 h = 0.0001 0.005 y[1] (numeric) = -2.28805477459 13.0485747498 y[1] (closed_form) = -2.2848351934 13.0507559192 absolute error = 0.003889 relative error = 0.02935 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1113 Order of pole (three term test) = 3005 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6356 2.352 h = 0.0001 0.003 y[1] (numeric) = -2.32561578301 13.1808153731 y[1] (closed_form) = -2.32274230331 13.1827547303 absolute error = 0.003467 relative error = 0.0259 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 914.2 Order of pole (three term test) = 3065 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6357 2.355 h = 0.001 0.001 y[1] (numeric) = -2.34751256164 13.2611423842 y[1] (closed_form) = -2.34459527038 13.2629210583 absolute error = 0.003417 relative error = 0.02537 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 726.3 Order of pole (three term test) = 3102 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6367 2.356 h = 0.001 0.003 y[1] (numeric) = -2.32911167454 13.2959629035 y[1] (closed_form) = -2.32619989077 13.297655419 absolute error = 0.003368 relative error = 0.02495 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3461 Order of pole (three term test) = 3114 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6377 2.359 h = 0.0001 0.004 y[1] (numeric) = -2.32687512301 13.3839986048 y[1] (closed_form) = -2.32395881632 13.3858674609 absolute error = 0.003464 relative error = 0.02549 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1982 Order of pole (three term test) = 3152 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6378 2.363 h = 0.003 0.006 y[1] (numeric) = -2.35676556044 13.4922716143 y[1] (closed_form) = -2.35397681445 13.4942219216 absolute error = 0.003403 relative error = 0.02484 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2669 Order of pole (three term test) = 3202 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6408 2.369 h = 0.0001 0.005 y[1] (numeric) = -2.32488153372 13.6795927288 y[1] (closed_form) = -2.32148371501 13.6818247851 absolute error = 0.004065 relative error = 0.02929 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1215 Order of pole (three term test) = 3280 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6409 2.374 h = 0.0001 0.003 y[1] (numeric) = -2.36266568358 13.8181892559 y[1] (closed_form) = -2.35963219602 13.8201724712 absolute error = 0.003624 relative error = 0.02585 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 998.3 Order of pole (three term test) = 3345 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.641 2.377 h = 0.001 0.001 y[1] (numeric) = -2.38465672495 13.9023668756 y[1] (closed_form) = -2.38157923814 13.904181703 absolute error = 0.003573 relative error = 0.02533 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 793.1 Order of pole (three term test) = 3386 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.642 2.378 h = 0.001 0.003 y[1] (numeric) = -2.36504378822 13.9385477693 y[1] (closed_form) = -2.36197301115 13.9402726281 absolute error = 0.003522 relative error = 0.02491 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3779 Order of pole (three term test) = 3399 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2542.0MB, alloc=52.3MB, time=30.78 x[1] = 0.643 2.381 h = 0.0001 0.004 y[1] (numeric) = -2.3617321107 14.0305131602 y[1] (closed_form) = -2.3586546533 14.0324222323 absolute error = 0.003622 relative error = 0.02545 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2164 Order of pole (three term test) = 3440 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6431 2.385 h = 0.003 0.006 y[1] (numeric) = -2.39176646394 14.1439805877 y[1] (closed_form) = -2.38882139573 14.1459761841 absolute error = 0.003558 relative error = 0.0248 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2914 Order of pole (three term test) = 3495 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6461 2.391 h = 0.0001 0.005 y[1] (numeric) = -2.35637633272 14.3393629538 y[1] (closed_form) = -2.35279170484 14.3416462081 absolute error = 0.00425 relative error = 0.02924 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1327 Order of pole (three term test) = 3580 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6462 2.396 h = 0.0001 0.003 y[1] (numeric) = -2.3943232143 14.4846034189 y[1] (closed_form) = -2.39112204392 14.4866306896 absolute error = 0.003789 relative error = 0.02581 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1090 Order of pole (three term test) = 3652 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6463 2.399 h = 0.001 0.001 y[1] (numeric) = -2.41637008191 14.5728056936 y[1] (closed_form) = -2.41312480146 14.5746565233 absolute error = 0.003736 relative error = 0.02529 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 866.1 Order of pole (three term test) = 3696 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6473 2.4 h = 0.001 0.003 y[1] (numeric) = -2.39547556479 14.6103946495 y[1] (closed_form) = -2.39223829252 14.612151543 absolute error = 0.003683 relative error = 0.02488 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4127 Order of pole (three term test) = 3710 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6483 2.403 h = 0.0001 0.004 y[1] (numeric) = -2.39099690991 14.7064543706 y[1] (closed_form) = -2.38775061583 14.7084036796 absolute error = 0.003787 relative error = 0.02541 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2363 Order of pole (three term test) = 3755 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6484 2.407 h = 0.003 0.006 y[1] (numeric) = -2.42112408236 14.8253511875 y[1] (closed_form) = -2.41801516667 14.8273923754 absolute error = 0.003719 relative error = 0.02476 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3182 Order of pole (three term test) = 3815 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6514 2.413 h = 0.0001 0.005 y[1] (numeric) = -2.38198099248 15.0291181305 y[1] (closed_form) = -2.3782005953 15.031452813 absolute error = 0.004443 relative error = 0.0292 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1449 Order of pole (three term test) = 3908 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6515 2.418 h = 0.0001 0.003 y[1] (numeric) = -2.4200242935 15.1813028373 y[1] (closed_form) = -2.4166474184 15.1833742845 absolute error = 0.003962 relative error = 0.02577 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1190 Order of pole (three term test) = 3986 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6516 2.421 h = 0.001 0.001 y[1] (numeric) = -2.44208489732 15.2737112057 y[1] (closed_form) = -2.43866388551 15.275597796 absolute error = 0.003907 relative error = 0.02526 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 945.7 Order of pole (three term test) = 4034 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2586.9MB, alloc=52.3MB, time=31.32 x[1] = 0.6526 2.422 h = 0.001 0.003 y[1] (numeric) = -2.41983561783 15.3127572839 y[1] (closed_form) = -2.4164240149 15.3145458064 absolute error = 0.003852 relative error = 0.02485 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4507 Order of pole (three term test) = 4050 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6536 2.425 h = 0.0001 0.004 y[1] (numeric) = -2.41409218547 15.4130823542 y[1] (closed_form) = -2.41066902325 15.415071837 absolute error = 0.003959 relative error = 0.02538 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2581 Order of pole (three term test) = 4099 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6537 2.429 h = 0.003 0.006 y[1] (numeric) = -2.44425618375 15.5376535212 y[1] (closed_form) = -2.44097555395 15.539740533 absolute error = 0.003888 relative error = 0.02472 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3475 Order of pole (three term test) = 4165 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6567 2.435 h = 0.0001 0.005 y[1] (numeric) = -2.40109861271 15.7501401563 y[1] (closed_form) = -2.39711308108 15.7525264084 absolute error = 0.004645 relative error = 0.02915 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1583 Order of pole (three term test) = 4265 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6568 2.44 h = 0.0001 0.003 y[1] (numeric) = -2.43916571719 15.9095821637 y[1] (closed_form) = -2.4356047538 15.9116978251 absolute error = 0.004142 relative error = 0.02573 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1300 Order of pole (three term test) = 4351 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6569 2.443 h = 0.001 0.001 y[1] (numeric) = -2.46119406761 16.0063857487 y[1] (closed_form) = -2.45758903286 16.0083077591 absolute error = 0.004085 relative error = 0.02522 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1033 Order of pole (three term test) = 4404 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6579 2.444 h = 0.0001 0.004 y[1] (numeric) = -2.43751301327 16.0469394028 y[1] (closed_form) = -2.43391889676 16.0487590436 absolute error = 0.004028 relative error = 0.02482 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6227 Order of pole (three term test) = 4421 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.658 2.448 h = 0.003 0.006 y[1] (numeric) = -2.46767130828 16.1763402782 y[1] (closed_form) = -2.46428470722 16.1785217204 absolute error = 0.004028 relative error = 0.02462 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3749 Order of pole (three term test) = 4492 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.661 2.454 h = 0.0001 0.005 y[1] (numeric) = -2.42094653271 16.3966625066 y[1] (closed_form) = -2.41682507872 16.3991484695 absolute error = 0.004813 relative error = 0.02904 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1708 Order of pole (three term test) = 4601 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6611 2.459 h = 0.0001 0.003 y[1] (numeric) = -2.45906262325 16.5626131744 y[1] (closed_form) = -2.45538458466 16.5648218697 absolute error = 0.00429 relative error = 0.02562 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1403 Order of pole (three term test) = 4693 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6612 2.462 h = 0.001 0.001 y[1] (numeric) = -2.48107878537 16.6633587567 y[1] (closed_form) = -2.47735670049 16.6653659136 absolute error = 0.004229 relative error = 0.0251 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1114 Order of pole (three term test) = 4750 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2631.8MB, alloc=52.3MB, time=31.87 x[1] = 0.6622 2.463 h = 0.001 0.003 y[1] (numeric) = -2.45611937715 16.7052699413 y[1] (closed_form) = -2.45240954778 16.7071708648 absolute error = 0.004168 relative error = 0.02469 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5310 Order of pole (three term test) = 4769 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6632 2.466 h = 0.0001 0.004 y[1] (numeric) = -2.44779632734 16.8140278922 y[1] (closed_form) = -2.44406976375 16.8161466697 absolute error = 0.004287 relative error = 0.02523 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3041 Order of pole (three term test) = 4826 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6633 2.47 h = 0.003 0.006 y[1] (numeric) = -2.47793663448 16.9498469249 y[1] (closed_form) = -2.47436272294 16.9520745183 absolute error = 0.004211 relative error = 0.02458 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4094 Order of pole (three term test) = 4904 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6663 2.476 h = 0.0001 0.005 y[1] (numeric) = -2.4266733121 17.1795486265 y[1] (closed_form) = -2.42232815858 17.1820862797 absolute error = 0.005032 relative error = 0.029 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1865 Order of pole (three term test) = 5023 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6664 2.481 h = 0.0001 0.003 y[1] (numeric) = -2.46466394666 17.353375872 y[1] (closed_form) = -2.46078520206 17.3556287137 absolute error = 0.004486 relative error = 0.02559 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1532 Order of pole (three term test) = 5124 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6665 2.484 h = 0.001 0.001 y[1] (numeric) = -2.48655348102 17.4588907483 y[1] (closed_form) = -2.48263094427 17.460932509 absolute error = 0.004422 relative error = 0.02507 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1217 Order of pole (three term test) = 5185 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6675 2.485 h = 0.001 0.003 y[1] (numeric) = -2.4600087931 17.502408202 y[1] (closed_form) = -2.4561002395 17.5043390924 absolute error = 0.004359 relative error = 0.02466 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5798 Order of pole (three term test) = 5206 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6685 2.488 h = 0.0001 0.004 y[1] (numeric) = -2.45010754614 17.6159594055 y[1] (closed_form) = -2.44617909274 17.6181177521 absolute error = 0.004482 relative error = 0.0252 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3321 Order of pole (three term test) = 5269 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6686 2.492 h = 0.003 0.006 y[1] (numeric) = -2.48009776705 17.758213207 y[1] (closed_form) = -2.47632761827 17.7604869496 absolute error = 0.004403 relative error = 0.02455 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4471 Order of pole (three term test) = 5353 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6716 2.498 h = 0.0001 0.005 y[1] (numeric) = -2.42398807065 17.997665489 y[1] (closed_form) = -2.41940859488 18.0002546764 absolute error = 0.005261 relative error = 0.02897 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2036 Order of pole (three term test) = 5483 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6717 2.503 h = 0.0001 0.003 y[1] (numeric) = -2.46176034289 18.1797217946 y[1] (closed_form) = -2.45767138599 18.1820185424 absolute error = 0.00469 relative error = 0.02556 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1673 Order of pole (three term test) = 5593 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2676.8MB, alloc=52.3MB, time=32.41 x[1] = 0.6718 2.506 h = 0.001 0.001 y[1] (numeric) = -2.48346471841 18.2902188324 y[1] (closed_form) = -2.47933234058 18.2922945307 absolute error = 0.004624 relative error = 0.02505 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1329 Order of pole (three term test) = 5661 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6728 2.507 h = 0.001 0.003 y[1] (numeric) = -2.45524573198 18.3353971558 y[1] (closed_form) = -2.4511291939 18.3373571577 absolute error = 0.004559 relative error = 0.02464 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6331 Order of pole (three term test) = 5683 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6738 2.51 h = 0.0001 0.004 y[1] (numeric) = -2.44364227678 18.4539394732 y[1] (closed_form) = -2.43950242477 18.4561369296 absolute error = 0.004687 relative error = 0.02518 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3626 Order of pole (three term test) = 5752 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6739 2.514 h = 0.003 0.006 y[1] (numeric) = -2.47340437428 18.6029154756 y[1] (closed_form) = -2.46942866052 18.6052352664 absolute error = 0.004603 relative error = 0.02453 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4882 Order of pole (three term test) = 5844 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6769 2.52 h = 0.0001 0.005 y[1] (numeric) = -2.4121225395 18.8525027068 y[1] (closed_form) = -2.40729764334 18.8551431475 absolute error = 0.0055 relative error = 0.02894 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2224 Order of pole (three term test) = 5986 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.677 2.525 h = 0.0001 0.003 y[1] (numeric) = -2.44957546645 19.0431553596 y[1] (closed_form) = -2.44526636659 19.0454956569 absolute error = 0.004904 relative error = 0.02554 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1826 Order of pole (three term test) = 6106 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6771 2.528 h = 0.001 0.001 y[1] (numeric) = -2.47103116557 19.1588563402 y[1] (closed_form) = -2.46667914306 19.160965176 absolute error = 0.004836 relative error = 0.02503 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1451 Order of pole (three term test) = 6180 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6781 2.529 h = 0.001 0.003 y[1] (numeric) = -2.44104425844 19.205751601 y[1] (closed_form) = -2.43671006913 19.207739718 absolute error = 0.004768 relative error = 0.02463 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6914 Order of pole (three term test) = 6204 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6791 2.532 h = 0.0001 0.004 y[1] (numeric) = -2.4276068222 19.3294904079 y[1] (closed_form) = -2.42324564076 19.3317263892 absolute error = 0.004901 relative error = 0.02516 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3959 Order of pole (three term test) = 6279 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6792 2.536 h = 0.003 0.006 y[1] (numeric) = -2.45705607068 19.485488091 y[1] (closed_form) = -2.45286504632 19.4878537211 absolute error = 0.004813 relative error = 0.0245 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5331 Order of pole (three term test) = 6380 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6822 2.542 h = 0.0001 0.005 y[1] (numeric) = -2.39025744325 19.7456082985 y[1] (closed_form) = -2.38517553309 19.7482995763 absolute error = 0.005751 relative error = 0.02891 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2428 Order of pole (three term test) = 6535 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2721.9MB, alloc=52.3MB, time=32.96 x[1] = 0.6823 2.547 h = 0.0001 0.003 y[1] (numeric) = -2.42728143837 19.9452399661 y[1] (closed_form) = -2.42274182275 19.9476233304 absolute error = 0.005127 relative error = 0.02552 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1994 Order of pole (three term test) = 6666 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6824 2.55 h = 0.001 0.001 y[1] (numeric) = -2.44841963427 20.0663759302 y[1] (closed_form) = -2.44383773197 20.0685169587 absolute error = 0.005057 relative error = 0.02502 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1584 Order of pole (three term test) = 6746 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6834 2.551 h = 0.0001 0.004 y[1] (numeric) = -2.41656635778 20.1150456777 y[1] (closed_form) = -2.41200442729 20.1170607615 absolute error = 0.004987 relative error = 0.02461 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9553 Order of pole (three term test) = 6773 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6835 2.555 h = 0.003 0.006 y[1] (numeric) = -2.44570350575 20.2770175003 y[1] (closed_form) = -2.44137542706 20.2794932501 absolute error = 0.004986 relative error = 0.02441 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5752 Order of pole (three term test) = 6882 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6865 2.561 h = 0.0001 0.005 y[1] (numeric) = -2.37399724147 20.5466052735 y[1] (closed_form) = -2.36874089435 20.549411312 absolute error = 0.005958 relative error = 0.0288 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2620 Order of pole (three term test) = 7049 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6866 2.566 h = 0.0001 0.003 y[1] (numeric) = -2.4106707529 20.7542914466 y[1] (closed_form) = -2.40598043563 20.7567825022 absolute error = 0.005311 relative error = 0.02542 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2152 Order of pole (three term test) = 7191 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6867 2.569 h = 0.001 0.001 y[1] (numeric) = -2.43154489939 20.8803030103 y[1] (closed_form) = -2.42681282435 20.8825419751 absolute error = 0.005235 relative error = 0.0249 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1710 Order of pole (three term test) = 7278 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6877 2.57 h = 0.001 0.003 y[1] (numeric) = -2.39802452092 20.9305713245 y[1] (closed_form) = -2.39331431578 20.9326796495 absolute error = 0.005161 relative error = 0.02449 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8146 Order of pole (three term test) = 7307 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6887 2.573 h = 0.0001 0.004 y[1] (numeric) = -2.38086340168 21.0645789362 y[1] (closed_form) = -2.37611873664 21.0669556961 absolute error = 0.005307 relative error = 0.02503 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4665 Order of pole (three term test) = 7395 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6888 2.577 h = 0.003 0.006 y[1] (numeric) = -2.40957293716 21.2344890757 y[1] (closed_form) = -2.40501023464 21.2370100852 absolute error = 0.005213 relative error = 0.02439 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6281 Order of pole (three term test) = 7514 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6918 2.583 h = 0.0001 0.005 y[1] (numeric) = -2.33165996579 21.5153928885 y[1] (closed_form) = -2.32612363208 21.5182487415 absolute error = 0.00623 relative error = 0.02878 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2861 Order of pole (three term test) = 7696 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2766.8MB, alloc=52.3MB, time=33.50 x[1] = 0.6919 2.588 h = 0.0001 0.003 y[1] (numeric) = -2.36768082006 21.7328146963 y[1] (closed_form) = -2.36273943532 21.7353476861 absolute error = 0.005553 relative error = 0.0254 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2350 Order of pole (three term test) = 7851 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.692 2.591 h = 0.001 0.001 y[1] (numeric) = -2.38809710886 21.8647180176 y[1] (closed_form) = -2.3831148831 21.8669871284 absolute error = 0.005475 relative error = 0.02489 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1867 Order of pole (three term test) = 7945 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.693 2.592 h = 0.001 0.003 y[1] (numeric) = -2.35251424628 21.9168732113 y[1] (closed_form) = -2.34755632023 21.9190060555 absolute error = 0.005397 relative error = 0.02448 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8895 Order of pole (three term test) = 7977 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.694 2.595 h = 0.0001 0.004 y[1] (numeric) = -2.33309812385 22.0567105411 y[1] (closed_form) = -2.32810121593 22.0591234982 absolute error = 0.005549 relative error = 0.02502 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5094 Order of pole (three term test) = 8073 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6941 2.599 h = 0.003 0.006 y[1] (numeric) = -2.3612155994 22.2345711956 y[1] (closed_form) = -2.3564072308 22.2371368988 absolute error = 0.00545 relative error = 0.02437 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6859 Order of pole (three term test) = 8203 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6971 2.605 h = 0.0001 0.005 y[1] (numeric) = -2.27669171305 22.5272306737 y[1] (closed_form) = -2.27086226233 22.5301354773 absolute error = 0.006513 relative error = 0.02876 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3124 Order of pole (three term test) = 8402 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6972 2.61 h = 0.0001 0.003 y[1] (numeric) = -2.31192273391 22.7548182702 y[1] (closed_form) = -2.30671853762 22.7573922967 absolute error = 0.005806 relative error = 0.02538 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2566 Order of pole (three term test) = 8571 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6973 2.613 h = 0.001 0.001 y[1] (numeric) = -2.33179532431 22.8928729702 y[1] (closed_form) = -2.3265513755 22.8951708103 absolute error = 0.005725 relative error = 0.02488 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2038 Order of pole (three term test) = 8675 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6983 2.614 h = 0.001 0.003 y[1] (numeric) = -2.29403641487 22.9469769647 y[1] (closed_form) = -2.28881936705 22.9491326854 absolute error = 0.005645 relative error = 0.02448 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9714 Order of pole (three term test) = 8709 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6993 2.617 h = 0.0001 0.004 y[1] (numeric) = -2.27219939736 23.0928809374 y[1] (closed_form) = -2.26693851321 23.0953289235 absolute error = 0.005803 relative error = 0.025 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5563 Order of pole (three term test) = 8814 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6994 2.621 h = 0.003 0.006 y[1] (numeric) = -2.29961013602 23.279042733 y[1] (closed_form) = -2.29454456936 23.2816524161 absolute error = 0.005698 relative error = 0.02436 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7490 Order of pole (three term test) = 8956 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2811.8MB, alloc=52.3MB, time=34.04 x[1] = 0.7024 2.627 h = 0.0001 0.005 y[1] (numeric) = -2.20804810052 23.5839127739 y[1] (closed_form) = -2.2019118221 23.5868654802 absolute error = 0.00681 relative error = 0.02875 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3411 Order of pole (three term test) = 9173 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7025 2.632 h = 0.0001 0.003 y[1] (numeric) = -2.24234118563 23.8221141171 y[1] (closed_form) = -2.23686191611 23.8247281124 absolute error = 0.006071 relative error = 0.02537 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2802 Order of pole (three term test) = 9358 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7026 2.635 h = 0.001 0.001 y[1] (numeric) = -2.2615775056 23.966590529 y[1] (closed_form) = -2.25605975725 23.9689154896 absolute error = 0.005988 relative error = 0.02487 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2226 Order of pole (three term test) = 9471 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7036 2.636 h = 0.001 0.003 y[1] (numeric) = -2.22152319935 24.0227067693 y[1] (closed_form) = -2.21603513495 24.0248835237 absolute error = 0.005904 relative error = 0.02447 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.061e+04 Order of pole (three term test) = 9509 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7046 2.639 h = 0.0001 0.004 y[1] (numeric) = -2.19708931884 24.1749231152 y[1] (closed_form) = -2.191552211 24.1774047796 absolute error = 0.006068 relative error = 0.02499 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6075 Order of pole (three term test) = 9623 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7047 2.643 h = 0.003 0.006 y[1] (numeric) = -2.22366960904 24.3697511587 y[1] (closed_form) = -2.2183348022 24.3724039482 absolute error = 0.005958 relative error = 0.02434 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8179 Order of pole (three term test) = 9778 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7077 2.649 h = 0.0001 0.005 y[1] (numeric) = -2.12461796023 24.6873023629 y[1] (closed_form) = -2.11816053912 24.6903017249 absolute error = 0.00712 relative error = 0.02873 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3725 Order of pole (three term test) = 1.002e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7078 2.654 h = 0.0001 0.003 y[1] (numeric) = -2.15781339311 24.9365838934 y[1] (closed_form) = -2.15204624969 24.9392366059 absolute error = 0.006348 relative error = 0.02536 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3060 Order of pole (three term test) = 1.022e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7079 2.657 h = 0.001 0.001 y[1] (numeric) = -2.17631371814 25.0877634687 y[1] (closed_form) = -2.1705095691 25.0901137351 absolute error = 0.006262 relative error = 0.02486 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2431 Order of pole (three term test) = 1.034e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7089 2.658 h = 0.0001 0.004 y[1] (numeric) = -2.13383860111 25.1459569281 y[1] (closed_form) = -2.12806711141 25.1481526589 absolute error = 0.006175 relative error = 0.02447 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.466e+04 Order of pole (three term test) = 1.038e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.709 2.662 h = 0.003 0.006 y[1] (numeric) = -2.15965553206 25.3481554256 y[1] (closed_form) = -2.15414423087 25.3509357802 absolute error = 0.006173 relative error = 0.02426 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8824 Order of pole (three term test) = 1.055e+04 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2856.8MB, alloc=52.3MB, time=34.58 x[1] = 0.712 2.668 h = 0.0001 0.005 y[1] (numeric) = -2.05393511154 25.6771083193 y[1] (closed_form) = -2.04725466078 25.6802386274 absolute error = 0.007377 relative error = 0.02864 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4019 Order of pole (three term test) = 1.080e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7121 2.673 h = 0.0001 0.003 y[1] (numeric) = -2.08618832926 25.9363313423 y[1] (closed_form) = -2.08022796309 25.9391077543 absolute error = 0.006575 relative error = 0.02527 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3301 Order of pole (three term test) = 1.102e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7122 2.676 h = 0.001 0.001 y[1] (numeric) = -2.10405411532 26.0935254807 y[1] (closed_form) = -2.09805801364 26.0959874131 absolute error = 0.006482 relative error = 0.02476 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2623 Order of pole (three term test) = 1.115e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7132 2.677 h = 0.001 0.003 y[1] (numeric) = -2.05941579942 26.1535911262 y[1] (closed_form) = -2.05345500142 26.1558928351 absolute error = 0.00639 relative error = 0.02435 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.250e+04 Order of pole (three term test) = 1.120e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7142 2.68 h = 0.0001 0.004 y[1] (numeric) = -2.02972713019 26.3182750847 y[1] (closed_form) = -2.02370675247 26.320906678 absolute error = 0.00657 relative error = 0.02489 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7157 Order of pole (three term test) = 1.133e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7143 2.684 h = 0.003 0.006 y[1] (numeric) = -2.05451377629 26.5302664725 y[1] (closed_form) = -2.04870938109 26.5330879972 absolute error = 0.006454 relative error = 0.02425 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9636 Order of pole (three term test) = 1.152e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7173 2.69 h = 0.0001 0.005 y[1] (numeric) = -1.94040088247 26.8728256221 y[1] (closed_form) = -1.93337093643 26.8759998706 absolute error = 0.007713 relative error = 0.02863 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4389 Order of pole (three term test) = 1.180e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7174 2.695 h = 0.0001 0.003 y[1] (numeric) = -1.97123193241 27.1440506463 y[1] (closed_form) = -1.9649583414 27.1468630766 absolute error = 0.006875 relative error = 0.02526 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3605 Order of pole (three term test) = 1.203e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7175 2.698 h = 0.001 0.001 y[1] (numeric) = -1.98815926765 27.3085041163 y[1] (closed_form) = -1.9818518194 27.310987543 absolute error = 0.006779 relative error = 0.02476 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2864 Order of pole (three term test) = 1.218e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7185 2.699 h = 0.001 0.003 y[1] (numeric) = -1.94085045143 27.3707736295 y[1] (closed_form) = -1.93458166779 27.3730900257 absolute error = 0.006683 relative error = 0.02435 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.365e+04 Order of pole (three term test) = 1.223e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7195 2.702 h = 0.0001 0.004 y[1] (numeric) = -1.90800413793 27.5425266843 y[1] (closed_form) = -1.90166944359 27.545187125 absolute error = 0.006871 relative error = 0.02488 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7816 Order of pole (three term test) = 1.238e+04 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2901.8MB, alloc=52.3MB, time=35.12 x[1] = 0.7196 2.706 h = 0.003 0.006 y[1] (numeric) = -1.93155631209 27.7643156601 y[1] (closed_form) = -1.92544519937 27.7671769575 absolute error = 0.006748 relative error = 0.02424 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.052e+04 Order of pole (three term test) = 1.257e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7226 2.712 h = 0.0001 0.005 y[1] (numeric) = -1.80852318447 28.1209993634 y[1] (closed_form) = -1.80112755532 28.1242156547 absolute error = 0.008065 relative error = 0.02862 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4793 Order of pole (three term test) = 1.288e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7227 2.717 h = 0.0001 0.003 y[1] (numeric) = -1.83773522207 28.4047498289 y[1] (closed_form) = -1.83113393548 28.4075964258 absolute error = 0.007189 relative error = 0.02525 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3937 Order of pole (three term test) = 1.314e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7228 2.72 h = 0.001 0.001 y[1] (numeric) = -1.85360153049 28.5767783628 y[1] (closed_form) = -1.84696851016 28.5792808005 absolute error = 0.007089 relative error = 0.02475 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3127 Order of pole (three term test) = 1.330e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7238 2.721 h = 0.001 0.003 y[1] (numeric) = -1.80347782738 28.6413211705 y[1] (closed_form) = -1.79688705894 28.6436495022 absolute error = 0.00699 relative error = 0.02436 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.490e+04 Order of pole (three term test) = 1.335e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7248 2.724 h = 0.0001 0.004 y[1] (numeric) = -1.76725370309 28.8204259241 y[1] (closed_form) = -1.76059025174 28.8231130264 absolute error = 0.007185 relative error = 0.02488 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8535 Order of pole (three term test) = 1.351e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7249 2.728 h = 0.003 0.006 y[1] (numeric) = -1.78940741316 29.0524389726 y[1] (closed_form) = -1.78297536292 29.0553384319 absolute error = 0.007055 relative error = 0.02424 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.149e+04 Order of pole (three term test) = 1.373e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7279 2.734 h = 0.0001 0.005 y[1] (numeric) = -1.65689684275 29.4237829651 y[1] (closed_form) = -1.64911863647 29.4270391373 absolute error = 0.008432 relative error = 0.02861 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5234 Order of pole (three term test) = 1.406e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.728 2.739 h = 0.0001 0.003 y[1] (numeric) = -1.68427838333 29.7206036459 y[1] (closed_form) = -1.67733430086 29.7234823145 absolute error = 0.007517 relative error = 0.02525 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4299 Order of pole (three term test) = 1.435e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7281 2.742 h = 0.001 0.001 y[1] (numeric) = -1.69895208563 29.9005358017 y[1] (closed_form) = -1.69197865616 29.903054498 absolute error = 0.007414 relative error = 0.02476 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3415 Order of pole (three term test) = 1.452e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7291 2.743 h = 0.001 0.003 y[1] (numeric) = -1.64586185393 29.9674228504 y[1] (closed_form) = -1.63893450318 29.9697600869 absolute error = 0.007311 relative error = 0.02436 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.627e+04 Order of pole (three term test) = 1.458e+04 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2946.9MB, alloc=52.3MB, time=35.66 x[1] = 0.7301 2.746 h = 0.0001 0.004 y[1] (numeric) = -1.60602673198 30.1541721619 y[1] (closed_form) = -1.59901945878 30.1568834818 absolute error = 0.007514 relative error = 0.02488 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9320 Order of pole (three term test) = 1.475e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7302 2.75 h = 0.003 0.006 y[1] (numeric) = -1.62660589534 30.3968531101 y[1] (closed_form) = -1.61983806662 30.3997888905 absolute error = 0.007377 relative error = 0.02423 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.255e+04 Order of pole (three term test) = 1.499e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7332 2.756 h = 0.0001 0.005 y[1] (numeric) = -1.48402970848 30.7834110221 y[1] (closed_form) = -1.47585129608 30.7867046289 absolute error = 0.008817 relative error = 0.02861 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5715 Order of pole (three term test) = 1.535e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7333 2.761 h = 0.0001 0.003 y[1] (numeric) = -1.50935373323 31.0938688224 y[1] (closed_form) = -1.50205109944 31.096777206 absolute error = 0.00786 relative error = 0.02525 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4694 Order of pole (three term test) = 1.566e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7334 2.764 h = 0.001 0.001 y[1] (numeric) = -1.52269370022 31.28204646 y[1] (closed_form) = -1.51536438854 31.2845783746 absolute error = 0.007754 relative error = 0.02476 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3729 Order of pole (three term test) = 1.585e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7344 2.765 h = 0.0001 0.004 y[1] (numeric) = -1.46647770041 31.3513502037 y[1] (closed_form) = -1.45919854762 31.3536930168 absolute error = 0.007647 relative error = 0.02436 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.248e+04 Order of pole (three term test) = 1.592e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7345 2.769 h = 0.003 0.006 y[1] (numeric) = -1.48564714127 31.603100358 y[1] (closed_form) = -1.47865292947 31.6061827935 absolute error = 0.007643 relative error = 0.02416 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.354e+04 Order of pole (three term test) = 1.617e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7375 2.775 h = 0.0001 0.005 y[1] (numeric) = -1.33410154645 32.003341284 y[1] (closed_form) = -1.32563897323 32.0067827902 absolute error = 0.009136 relative error = 0.02852 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6166 Order of pole (three term test) = 1.656e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7376 2.78 h = 0.0001 0.003 y[1] (numeric) = -1.35763224824 32.3260374232 y[1] (closed_form) = -1.35008278236 32.3290866241 absolute error = 0.008142 relative error = 0.02516 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5065 Order of pole (three term test) = 1.690e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7377 2.783 h = 0.001 0.001 y[1] (numeric) = -1.36980747138 32.5216151323 y[1] (closed_form) = -1.36223365852 32.5242730588 absolute error = 0.008027 relative error = 0.02466 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4024 Order of pole (three term test) = 1.710e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7387 2.784 h = 0.001 0.003 y[1] (numeric) = -1.31079732499 32.5930982086 y[1] (closed_form) = -1.3032773012 32.5955601646 absolute error = 0.007913 relative error = 0.02426 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.917e+04 Order of pole (three term test) = 1.717e+04 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2991.9MB, alloc=52.3MB, time=36.20 x[1] = 0.7397 2.787 h = 0.0001 0.004 y[1] (numeric) = -1.26367461323 32.7949383942 y[1] (closed_form) = -1.25606005677 32.7978046616 absolute error = 0.008136 relative error = 0.02479 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.098e+04 Order of pole (three term test) = 1.738e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7398 2.791 h = 0.003 0.006 y[1] (numeric) = -1.28095117323 33.0587374992 y[1] (closed_form) = -1.27359179796 33.0618523544 absolute error = 0.007991 relative error = 0.02415 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.478e+04 Order of pole (three term test) = 1.766e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7428 2.797 h = 0.0001 0.005 y[1] (numeric) = -1.11816471421 33.4752796833 y[1] (closed_form) = -1.10926703403 33.4787534751 absolute error = 0.009552 relative error = 0.02852 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6734 Order of pole (three term test) = 1.809e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7429 2.802 h = 0.0001 0.003 y[1] (numeric) = -1.13917827287 33.8127327396 y[1] (closed_form) = -1.13123906689 33.8158067165 absolute error = 0.008514 relative error = 0.02516 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5531 Order of pole (three term test) = 1.845e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.743 2.805 h = 0.001 0.001 y[1] (numeric) = -1.14973420728 34.0172311301 y[1] (closed_form) = -1.14177389475 34.0198959849 absolute error = 0.008395 relative error = 0.02466 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4394 Order of pole (three term test) = 1.867e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.744 2.806 h = 0.001 0.003 y[1] (numeric) = -1.08728142975 34.0912718013 y[1] (closed_form) = -1.07937949355 34.0937324776 absolute error = 0.008276 relative error = 0.02426 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.094e+04 Order of pole (three term test) = 1.875e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.745 2.809 h = 0.0001 0.004 y[1] (numeric) = -1.03580625513 34.3016572074 y[1] (closed_form) = -1.02780106078 34.3045393117 absolute error = 0.008508 relative error = 0.02479 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.199e+04 Order of pole (three term test) = 1.897e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7451 2.813 h = 0.003 0.006 y[1] (numeric) = -1.05093706076 34.5774981746 y[1] (closed_form) = -1.04319575793 34.5806428611 absolute error = 0.008356 relative error = 0.02415 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.614e+04 Order of pole (three term test) = 1.928e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7481 2.819 h = 0.0001 0.005 y[1] (numeric) = -0.876224171662 35.0109494316 y[1] (closed_form) = -0.866871479886 35.0144521398 absolute error = 0.009987 relative error = 0.02851 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7353 Order of pole (three term test) = 1.975e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7482 2.824 h = 0.0001 0.003 y[1] (numeric) = -0.894444040764 35.3637944744 y[1] (closed_form) = -0.886097311221 35.3668900233 absolute error = 0.008902 relative error = 0.02516 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6040 Order of pole (three term test) = 2.015e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7483 2.827 h = 0.001 0.001 y[1] (numeric) = -0.903209124762 35.5775963691 y[1] (closed_form) = -0.894844872337 35.5802641824 absolute error = 0.008779 relative error = 0.02467 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4798 Order of pole (three term test) = 2.039e+04 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3036.9MB, alloc=52.3MB, time=36.74 x[1] = 0.7493 2.828 h = 0.001 0.003 y[1] (numeric) = -0.837130725794 35.6542714004 y[1] (closed_form) = -0.828829733946 35.656726509 absolute error = 0.008656 relative error = 0.02427 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.286e+04 Order of pole (three term test) = 2.047e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7503 2.831 h = 0.0001 0.004 y[1] (numeric) = -0.781012898437 35.8735377067 y[1] (closed_form) = -0.77259934141 35.8764320321 absolute error = 0.008897 relative error = 0.02479 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.309e+04 Order of pole (three term test) = 2.072e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7504 2.835 h = 0.003 0.006 y[1] (numeric) = -0.793768163269 36.1619377454 y[1] (closed_form) = -0.78562744438 36.1651093725 absolute error = 0.008737 relative error = 0.02415 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.763e+04 Order of pole (three term test) = 2.105e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7534 2.841 h = 0.0001 0.005 y[1] (numeric) = -0.606405748694 36.6129256014 y[1] (closed_form) = -0.596577283835 36.6164534849 absolute error = 0.01044 relative error = 0.02851 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8029 Order of pole (three term test) = 2.156e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7535 2.846 h = 0.0001 0.003 y[1] (numeric) = -0.621535924548 36.9818231659 y[1] (closed_form) = -0.612763124587 36.9849367415 absolute error = 0.009309 relative error = 0.02517 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6595 Order of pole (three term test) = 2.200e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7536 2.849 h = 0.001 0.001 y[1] (numeric) = -0.628326649251 37.2053266848 y[1] (closed_form) = -0.619540277236 37.2079931149 absolute error = 0.009182 relative error = 0.02467 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5239 Order of pole (three term test) = 2.226e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7546 2.85 h = 0.001 0.003 y[1] (numeric) = -0.558430567905 37.2847142627 y[1] (closed_form) = -0.549712654559 37.2871591332 absolute error = 0.009054 relative error = 0.02428 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.497e+04 Order of pole (three term test) = 2.235e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7556 2.853 h = 0.0001 0.004 y[1] (numeric) = -0.497363143832 37.5132090144 y[1] (closed_form) = -0.488522743145 37.5161115863 absolute error = 0.009305 relative error = 0.0248 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.430e+04 Order of pole (three term test) = 2.262e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7557 2.857 h = 0.003 0.006 y[1] (numeric) = -0.507497030156 37.8147060232 y[1] (closed_form) = -0.498938653095 37.8179013769 absolute error = 0.009135 relative error = 0.02415 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.925e+04 Order of pole (three term test) = 2.299e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7587 2.863 h = 0.0001 0.005 y[1] (numeric) = -0.306722560828 38.2838781851 y[1] (closed_form) = -0.296396670171 38.2874271047 absolute error = 0.01092 relative error = 0.02852 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8768 Order of pole (three term test) = 2.354e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7588 2.868 h = 0.0001 0.003 y[1] (numeric) = -0.318446426278 38.6695152009 y[1] (closed_form) = -0.309228215137 38.6726428936 absolute error = 0.009734 relative error = 0.02517 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7202 Order of pole (three term test) = 2.402e+04 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3081.9MB, alloc=52.3MB, time=37.28 x[1] = 0.7589 2.871 h = 0.001 0.001 y[1] (numeric) = -0.32306662946 38.903134316 y[1] (closed_form) = -0.313839189562 38.9057946249 absolute error = 0.009603 relative error = 0.02468 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5721 Order of pole (three term test) = 2.431e+04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7599 2.872 h = 0.001 0.003 y[1] (numeric) = -0.249151310899 38.9853140123 y[1] (closed_form) = -0.239997859357 38.9877435665 absolute error = 0.00947 relative error = 0.02429 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.726e+04 Order of pole (three term test) = 2.441e+04 0 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) * cos ( x ) ; Iterations = 754 Total Elapsed Time = 37 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 37 Seconds > quit memory used=3093.4MB, alloc=52.3MB, time=37.42